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3.0

Jun 30, 2018
06/18

by
Junbeom Lee; Chao Zhou

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In this paper, we investigate conditions to represent derivative price under XVA explicitly. As long as we consider different borrowing/lending rates, XVA problem becomes a non-linear equa- tion and this makes finding explicit solution of XVA difficult. It is shown that the associated valuation problem is actually linear under some proper conditions so that we can have the same complexity in pricing as classical pricing theory. Moreover, the conditions mentioned above is mild in the sense that...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.00259

6
6.0

Jun 30, 2018
06/18

by
Kim Weston

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We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity. After establishing the existence of a discrete-time equilibrium, we show that the discrete-time equilibrium converges to a continuous-time equilibrium model. The continuous-time equilibrium provides an explicit formula for the equilibrium interest rate in terms of...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1702.01706

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8.0

Jun 30, 2018
06/18

by
Alessandra Cretarola; Gianna Figà Talamanca

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We endorse the idea, suggested in recent literature, that BitCoin prices are influenced by sentiment and confidence about the underlying technology; as a consequence, an excitement about the BitCoin system may propagate to BitCoin prices causing a Bubble effect, the presence of which is documented in several papers about the cryptocurrency. In this paper we develop a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as the behavior of a second factor...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1702.00215

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6.0

Jun 29, 2018
06/18

by
David Hobson; Anthony Neuberger

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The purpose of this note is to reconcile two different results concerning the model-free upper bound on the price of an American option, given a set of European option prices. Neuberger (2007, `Bounds on the American option') and Hobson and Neuberger (2016, `On the value of being American') argue that the cost of the cheapest super-replicating strategy is equal to the highest model-based price, where we search over all models which price correctly the given European options. Bayraktar, Huang...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1604.02274

9
9.0

Jun 29, 2018
06/18

by
Gunther Leobacher; Michaela Szölgyenyi; Stefan Thonhauser

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We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant and observable volatility and constant but unknown drift parameter. For transforming the problem to a problem with complete information, we derive a suitable filter. The optimal value function is characterized as the unique viscosity solution of the associated...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.04660

8
8.0

Jun 29, 2018
06/18

by
Candia Riga

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This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a pathwise self-financial condition for continuous-time trading strategies, which is consistent with the classical definition in case a probability model is introduced. Our first...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.04946

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14

Jun 30, 2018
06/18

by
Tim Leung; Hongzhong Zhang

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Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject to a trailing stop. Under a general linear diffusion framework, we study an optimal double stopping problem with a random path-dependent maturity. Specifically, we first derive the optimal liquidation strategy prior to a given trailing stop, and prove the...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1701.03960

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56

Jun 27, 2018
06/18

by
Michael V. Klibanov; Andrey V. Kuzhuget

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A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved as a parabolic equation with the reversed time, which is an ill-posed problem. Thus, a regularization method is used to solve it. This idea is verified on real market data for...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1503.03567

8
8.0

Jun 29, 2018
06/18

by
Francesca Biagini; Yinglin Zhang

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In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space. Such a model guarantees not only the positivity of the OIS short rate and the mortality intensity, but also the possibility of approximating both pricing formula and hedging strategy of a large class of life insurance products by explicit...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.07910

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6.0

Jun 29, 2018
06/18

by
Aleš Černý

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We examine optimal quadratic hedging of barrier options in a discretely sampled exponential L\'{e}vy model that has been realistically calibrated to reflect the leptokurtic nature of equity returns. Our main finding is that the impact of hedging errors on prices is several times higher than the impact of other pricing biases studied in the literature.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1603.03747

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8.0

Jun 29, 2018
06/18

by
Nuno Azevedo; Diogo Pinheiro; Stylianos Xanthopoulos; Athanasios Yannacopoulos

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Within the setup of continuous-time semimartingale financial markets, we show that a multiprior Gilboa-Schmeidler minimax expected utility maximizer forms a portfolio consisting only of the riskless asset if and only if among the investor's priors there exists a probability measure under which all admissible wealth processes are supermartingales. Furthermore, we show that under a certain attainability condition (which is always valid in finite or complete markets) this is also equivalent to the...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.02446

7
7.0

Jun 29, 2018
06/18

by
Zdzislaw Brzezniak; Tayfun Kok

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In this paper we study the stochastic evolution equation (1.1) in martingale-type 2 Banach spaces (with the linear part of the drift being only a generator of a C0-semigroup). We prove the existence and the uniqueness of solutions to this equation. We apply the abstract results to the Heath-Jarrow-Morton-Musiela (HJMM) equation (6.3). In particular, we prove the existence and the uniqueness of solutions to the latter equation in the weighted Lebesgue and Sobolev spaces respectively. We also...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.05814

7
7.0

Jun 29, 2018
06/18

by
Kristoffer Lindensjö

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The optimal investment problem is one of the most important problems in mathematical finance. The main contribution of the present paper is an explicit formula for the optimal portfolio process. Our optimal investment problem is that of maximizing the expected value of a standard general utility function of terminal wealth in a standard complete Wiener driven financial market. In order to derive the formula for the optimal portfolio we use the recently developed functional It\^o calculus and...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1610.05018

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12

Jun 27, 2018
06/18

by
Takuji Arai

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We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk measure a good deal valuation; and study its properties. We also discuss superhedging cost and Fundamental Theorem of Asset Pricing for convex constrained markets.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1506.00396

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5.0

Jun 30, 2018
06/18

by
Xiaoxiao Zheng; Xin Zhang

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In this paper, we consider the optimal dividend problem for a company. We describe the surplus process of the company by a diffusion model with regime switching. The aim of the company is to choose a dividend policy to maximize the expected total discounted payments until ruin. In this article, we consider a hybrid dividend strategy, that is, the company is allowed to conduct continuous dividend strategy as well as impulsive dividend strategy. In addition, we consider the change of economy,...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1406.7606

6
6.0

Jun 28, 2018
06/18

by
Gechun Liang; Thaleia Zariphopoulou

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In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive optimization. In addition, we develop a connection, for large time horizons, with a family of classical...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1511.04863

12
12

Jun 27, 2018
06/18

by
Huiwen Yan; Zhou Yang; Fahuai Yi; Gechun Liang

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This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint, and then in a Markovian setting, we investigate the optimal strategy by analyzing the properties of the corresponding free boundary, including its position, asymptotics, monotonicity and regularity. We...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1503.08961

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20

Jun 27, 2018
06/18

by
Si Cheng; Michael R. Tehranchi

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In this article, we explore a class of tractable interest rate models that have the property that the price of a zero-coupon bond can be expressed as a polynomial of a state diffusion process. Our results include a classification of all such time-homogeneous single-factor models in the spirit of Filipovic's maximal degree theorem for exponential polynomial models, as well as an explicit characterisation of the set of feasible parameters in the case when the factor process is bounded. Extensions...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1504.03238

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15

Jun 27, 2018
06/18

by
Ramin Okhrati; Alejandro Balbás; José Garrido

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In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on no prior default. More precisely, in this particular framework, the locally risk-minimizing approach is carried out when the underlying process has jumps, the derivative is...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1505.03501

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21

Jun 27, 2018
06/18

by
Tim Leung; Kazutoshi Yamazaki; Hongzhong Zhang

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We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence the solutions in general cannot be attained analytically. Motivated by the maturity randomization (Canadization) technique by Carr (1998), we approximate the refraction times by...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1505.07705

9
9.0

Jun 30, 2018
06/18

by
Kasper Larsen; Halil Mete Soner; Gordan Žitković

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We introduce the notion of a conditional Davis price and study its properties. Our ultimate goal is to use utility theory to price non-replicable contingent claims in the case when the investor's portfolio already contains a non-replicable component. We show that even in the simplest of settings - such as Samuelson's model - conditional Davis prices are typically not unique and form a non-trivial subinterval of the set of all no-arbitrage prices. Our main result characterizes this set and...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1702.02087

7
7.0

Jun 30, 2018
06/18

by
Sabrina Mulinacci

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In this paper we study the distributional properties of a vector of lifetimes in which each lifetime is modeled as the first arrival time between an idiosyncratic shock and a common systemic shock. Despite unlike the classical multidimensional Marshall-Olkin model here only a unique common shock affecting all the lifetimes is assumed, some dependence is allowed between each idiosyncratic shock arrival time and the systemic shock arrival time. The dependence structure of the resulting...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1704.02160

9
9.0

Jun 29, 2018
06/18

by
Yuki Shigeta

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In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional RBSDEs) and show that a value function of the optimal switching under ambiguity coincides with a solutions to multidimensional RBSDEs with allowing negative switching costs. Furthermore, we naturally extend the finite horizon problem to the infinite horizon...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.06045

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6.0

Jun 30, 2018
06/18

by
Johan GB Beumee; Chris Cormack; Peyman Khorsand; Manish Patel

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This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process in velocity space which also preserves the proper state equation of motion. Many numerical numerical examples of this process are provided. For a smaller grid the probability construction converges into a...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1406.0077

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17

Jun 28, 2018
06/18

by
Erik Ekström; Juozas Vaicenavicius

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We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability distribution to characterise the uncertainty about the drift parameter. Filtering theory is used to describe the evolution of the posterior beliefs about the drift once the price process is being observed. An optimal stopping time is determined as the first...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1509.00686

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11

Jun 27, 2018
06/18

by
Archil Gulisashvili; Frederi Viens; Xin Zhang

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We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small-time behaviors of the above depend heavily on the model, and require a control of the asset price density which is uniform with respect to the asset price variable, in order to...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1505.05256

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17

Jun 28, 2018
06/18

by
Dmitry Kramkov; Kim Weston

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In the problem of optimal investment with utility function defined on $(0,\infty)$, we formulate sufficient conditions for the dual optimizer to be a uniformly integrable martingale. Our key requirement consists of the existence of a martingale measure whose density process satisfies the probabilistic Muckenhoupt $(A_p)$ condition for the power $p=1/(1-a)$, where $a\in (0,1)$ is a lower bound on the relative risk-aversion of the utility function. We construct a counterexample showing that this...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1507.05865

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7.0

Jun 30, 2018
06/18

by
Tim Leung; Xin Li; Zheng Wang

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This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and switching problems admit the same optimal starting and/or stopping strategies. We rigorously prove that the optimal starting and stopping strategies are of threshold type, and give the analytical...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1411.6080

7
7.0

Jun 30, 2018
06/18

by
Andrei Lebedev; Petr Zabreiko

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In the article a strenthened version of the 'Fundamental Theorem of asset Pricing' for one-period market model is proven. The principal role in this result play total and nonanihilating cones.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1412.7058

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3.0

Jun 30, 2018
06/18

by
Wai-Ki Ching; Jia-Wen Gu; Harry Zheng

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In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market participants includes the default time of each firm and the periodic asset value reports. In this situation, the default time of each firm becomes a totally inaccessible stopping time to the market participants. The original structural model is first...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1409.1393

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5.0

Jun 30, 2018
06/18

by
Wei Lin; Shenghong Li; Shane Chern

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In this paper, we relax the power parameter of instantaneous variance and develop a new stochastic volatility plus jumps model that generalize the Heston model and 3/2 model as special cases. This model has two distinctive features. First, we do not restrict the new parameter, letting the data speak as to its direction. The Generalized Methods of Moments suggests that the newly added parameter is to create varying volatility fluctuation in different period discovered in financial market....

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.06020

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9.0

Jun 29, 2018
06/18

by
Francesca Biagini; Andrea Mazzon; Thilo Meyer-Brandis

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We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in the work of Jarrow, Protter and Roch (2012). To justify $W^F$ from a fundamental point of view, we embed this constructive approach in the martingale theory of bubbles, see Jarrow, Protter and Shimbo (2010) and Biagini, F\"ollmer and Nedelcu (2014), by showing the existence of a flow...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1611.01440

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13

Jun 28, 2018
06/18

by
Matteo Burzoni; Marco Frittelli; Marco Maggis

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In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path $\omega \in \Omega$, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1506.06608

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11

Jun 30, 2018
06/18

by
Tomasz R. Bielecki; Marek Rutkowski

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The research presented in this work is motivated by recent papers by Brigo et al. (2011), Burgard and Kjaer (2009), Cr\'epey (2012), Fujii and Takahashi (2010), Piterbarg (2010) and Pallavicini et al. (2012). Our goal is to provide a sound theoretical underpinning for some results presented in these papers by developing a unified framework for the non-linear approach to hedging and pricing of OTC financial contracts. We introduce a systematic approach to valuation and hedging in nonlinear...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1405.4079

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13

Jun 28, 2018
06/18

by
Josselin Garnier; George Papanicolaou; Tzu-Wei Yang

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We formulate and analyze a multi-agent model for the evolution of individual and systemic risk in which the local agents interact with each other through a central agent who, in turn, is influenced by the mean field of the local agents. The central agent is stabilized by a bistable potential, the only stabilizing force in the system. The local agents derive their stability only from the central agent. In the mean field limit of a large number of local agents we show that the systemic risk...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1507.08333

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4.0

Jun 30, 2018
06/18

by
Samuel Drapeau; Peng Luo; Dewen Xiong

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We characterize a class of fully coupled forward backward stochastic differential equations in terms of optimal maximal sub-solutions of BSDEs. We present the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We provide some explicit examples and show how to quantify the costs of incompleteness when using utility indifference pricing.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.02694

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4.0

Jun 30, 2018
06/18

by
Tianyang Nie; Marek Rutkowski

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Our previous results are extended to the case of the margin account, which may depend on the contract's value for the hedger and/or the counterparty. The present work generalizes also the papers by Bergman (1995), Mercurio (2013) and Piterbarg (2010). Using the comparison theorems for BSDEs, we derive inequalities for the unilateral prices and we give the range for its fair bilateral prices. We also establish results yielding the link to the market model with a single interest rate. In the case...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1412.2453

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6.0

Jun 30, 2018
06/18

by
Ralph Rudd; Thomas A. McWalter; Joerg Kienitz; Eckhard Platen

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Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is usually performed using stochastic methods, e.g., Lloyd's algorithm or Competitive Learning Vector Quantization. In this paper, a new algorithm is proposed that allows RMQ to be applied to two-factor stochastic volatility models, which retains the efficiency of...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1704.06388

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8.0

Jun 28, 2018
06/18

by
Takanori Adachi

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We introduce a formal language IE that is a variant of the language PAL developed in [van Benthem 2011] by adding a belief operator and a common belief operator,specializing to stochastic analysis. A constant symbol in the language denotes a stochastic process so that we can represent several financial events as formulae in the language, which is expected to be clues of analyzing the moments that some stochastic jumps such as financial crises occur based on knowledge and belief of individuals...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.00227

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4.0

Jun 28, 2018
06/18

by
Robert Fernholz

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Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these markets are given: i) a market with a singular covariance matrix and instantaneous relative arbitrage; ii) a market with a singular covariance matrix and no arbitrage; iii) a market with a nonsingular covariance matrix and no arbitrage; iv) a market with a...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.02478

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9.0

Jun 29, 2018
06/18

by
Carol Alexander; Johannes Rauch

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Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are initially characterised as solutions to a second-order system of PDEs, then those pay-offs based on martingale and log-martingale processes alone form a vector space. Hence there exist an infinite variety of other variance and higher-moment risk premia that are...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.00235

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5.0

Jun 29, 2018
06/18

by
Philip Ernst; Larry Shepp

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Using a bondholder who seeks to determine when to sell his bond as our motivating example, we revisit one of Larry Shepp's classical theorems on optimal stopping. We offer a novel proof of Theorem 1 from from \cite{Shepp}. Our approach is that of guessing the optimal control function and proving its optimality with martingales. Without martingale theory one could hardly prove our guess to be correct.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1605.00762

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8.0

Jun 29, 2018
06/18

by
Claudia Ceci; Katia Colaneri; Alessandra Cretarola

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In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. We assume that the stock price process dynamics depends on an...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.07226

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6.0

Jun 29, 2018
06/18

by
Hannes Hoffmann; Thilo Meyer-Brandis; Gregor Svindland

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We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate case in F\"ollmer (2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1609.07903

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8.0

Jun 29, 2018
06/18

by
K. Kanjamapornkul; R. Pinčák

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We provide the proof that the space of time series data is a Kolmogorov space with $T_{0}$-separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes from the rotation of data around price and time axis by defining a new extradimension to time series data. We show that there exist hidden eight dimensions in Kolmogorov space for...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1606.03901

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6.0

Jun 29, 2018
06/18

by
Vladimir Vovk; Glenn Shafer

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This paper gives yet another definition of game-theoretic probability in the context of continuous-time idealized financial markets. Without making any probabilistic assumptions (but assuming positive and continuous price paths), we obtain a simple expression for the equity premium and derive a version of the capital asset pricing model.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1607.00830

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5.0

Jun 28, 2018
06/18

by
Mourad Lazgham

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We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic programming principle, which allows us to derive conditions under which a classical solution of the HJB equation coincides with our value function (provided that it is smooth enough)....

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1510.03584

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9.0

Jun 28, 2018
06/18

by
Robert Fernholz

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Long-term relative arbitrage exists in markets where the excess growth rate of the market portfolio is bounded away from zero. Here it is shown that under a time-homogeneity hypothesis this condition will also imply the existence of relative arbitrage over arbitrarily short intervals.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1510.02292

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Jun 27, 2018
06/18

by
Mykhaylo Shkolnikov; Ronnie Sircar; Thaleia Zariphopoulou

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We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We analyze the associated forward performance SPDE and provide explicit formulae for the leading order and first order correction terms for the forward investment process and the...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1504.03209

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8.0

Jun 29, 2018
06/18

by
David Hobson; Alex S. L. Tse; Yeqi Zhu

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In this article we consider the Merton problem in a market with a single risky asset and transaction costs. We give a complete solution of the problem up to the solution of a free-boundary problem for a first-order differential equation, and find that the form of the solution (whether the problem is well-posed, whether the problem is well-posed only for large transaction costs, whether the no-transaction wedge lies in the first, second or fourth quadrants) depends only on a quadratic whose...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1612.00720