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作者：Kazi-Tani, Nabil; Possamai, Dylan; Zhou, Chao
作者单位：Universite Claude Bernard Lyon 1; Universite PSL; Universite Paris-Dauphine; National University of Singapore
摘要：In this paper, we define a notion of second-order backward stochastic differential equations with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190]. However, on the contrary to their formulation, where they can define pathwise the density of quadratic variation of the canonical process, in our setting, the compensator of the jump measure associated to the jumps of the canonical process, which...
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作者：Bank, Peter; Kramkov, Dmitry
作者单位：Technical University of Berlin; Carnegie Mellon University
摘要：We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the investor's orders and trade among themselves to attain Pareto optimal allocations. We first consider the case of simple strategies and then, in analogy to the construction of stochastic integrals, investigate the transition to general continuous dynamics. A...
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作者：Georgiou, Nicos; Joseph, Mathew; Khoshnevisan, Davar; Shiu, Shang-Yuan
作者单位：University of Sussex; University of Sheffield; Utah System of Higher Education; University of Utah; National Central University
摘要：Consider an infinite system partial derivative(t)u(t) (x) = (Lu-t) (x) + sigma (u(t) (x)) partial derivative(t) B-t (x) of interacting Ito diffusions, started at a nonnegative deterministic bounded initial profile. We study local and global features of the solution under standard regularity assumptions on the nonlinearity sigma. We will show that, locally in time, the solution behaves as a collection of independent diffusions. We prove also that the kth moment Lyapunov exponent is frequently o...
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作者：Lionnet, Arnaud; Dos Reis, Goncalo; Szpruch, Lukasz
作者单位：University of Oxford; University of Edinburgh
摘要：In this paper, we undertake the error analysis of the time discretization of systems of Forward Backward Stochastic Differential Equations (FBSDEs) with drivers having polynomial growth and that are also monotone in the state variable. We show with a counter-example that the natural explicit Euler scheme may diverge, unlike in the canonical Lipschitz driver case. This is due to the lack of a certain stability property of the Euler scheme which is essential to obtain convergence. However, a tho...
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作者：Dupuis, Paul; Spiliopoulos, Konstantinos; Zhou, Xiang
作者单位：Brown University; Boston University; City University of Hong Kong
摘要：We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complicates the analysis is that rest points are included in the domain of interest. We build importance sampling schemes with provably good performance both pre-asymptotically, that is, for fixed size of the noise, and asymptotically, that is, as the size of the noise goes to zero, and that do not degrade as the time horiz...
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作者：Rebeschini, Patrick; van Handel, Ramon
作者单位：Princeton University
摘要：The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the underlying model. This phenomenon has rendered particle filters of limited use in complex data assimilation problems. In this paper, we argue that it is often possible, at least in principle, to develop local particle filtering algorithms whose approximation error ...
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作者：Nutz, Marcel; Zhang, Jianfeng
作者单位：Columbia University; University of Southern California
摘要：We study the existence of optimal actions in a zero-sum game inf(tau) sup(P) E-P [X-tau] between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem inf(tau) epsilon(X-tau) for a class of sublinear expectations epsilon(.) such as the G-expectation. We show that the game has a value. Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope Y and prove that the first hitting time inf{t : Y-t = X-t} is an opt...
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作者：Stauffer, Alexandre
作者单位：University of Bath
摘要：Consider the model where nodes are initially distributed as a Poisson point process with intensity lambda over R-d and are moving in continuous time according to independent Brownian motions. We assume that nodes are capable of detecting all points within distance r of their location and study the problem of determining the first time at which a target particle, which is initially placed at the origin of R-d, is detected by at least one node. We consider the case where the target particle can ...
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作者：Possamai, Dylan; Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both robustness properties of BSDEs, as proved in Briand, Delyon and Memin [Stochastic Process. Appl. 97 (2002) 229-253], and tightness of solutions to discrete time BSDEs. In particular, when the approximating martingales are given by some particular controlled Markov ch...
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作者：Henard, Olivier
作者单位：University of London; Queen Mary University London
摘要：We define a Markov process in a forward population model with backward genealogy given by the Lambda-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two applications are discussed. The probability that the n-coalescent is deeper than the (n - 1)-coalescent is studied. The distribution of the number of blocks in the last coalescence of the n-Beta(2 - alpha, alpha)-coalescent is proved to converge as n -> infinity, an...
