Backward stochastic differential equations with reflection and Dynkin games
Jakša Cvitanić,Ioannis Karatzas +1 more
TLDR
In this article, the authors established existence and uniqueness results for adapted solutions of backward stochastic differential equations with two reflecting barriers, generalizing the work of El Karoui, Kapoudjian, Pardoux, Peng and Quenez.Abstract:
We establish existence and uniqueness results for adapted solutions of backward stochastic differential equations (BSDE's) with two reflecting barriers, generalizing the work of El Karoui, Kapoudjian, Pardoux, Peng and Quenez. Existence is proved first by solving a related pair of coupled optimal stopping problems, and then, under different conditions, via a penalization method. It is also shown that the solution coincides with the value of a certain Dynkin game, a stochastic game of optimal stopping. Moreover, the connection with the backward SDE enables us to provide a pathwise (deterministic) approach to the game.read more
Citations
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Book ChapterDOI
Nonlinear Expectations, Nonlinear Evaluations and Risk Measures
TL;DR: In this article, the authors propose a mechanism of evaluating risky assets using axiomatic assumptions for evaluating derivatives of derivatives, which is based on the Brownian Filtration Consistent Evaluations and Expectations.
Journal ArticleDOI
Second-Order Backward Stochastic Differential Equations and Fully Nonlinear Parabolic PDEs
TL;DR: In this article, the existence and uniqueness of adapted processes Y, Z, Ŵ, and A solving the second-order backward stochastic differential equation (2BSDE) was studied.
Journal ArticleDOI
On the Starting and Stopping Problem: Application in Reversible Investments
Said Hamadène,Monique Jeanblanc +1 more
TL;DR: This work solves completely the starting and stopping problem when the dynamics of the system are a general adapted stochastic process and uses backward stoChastic differential equations and Snell envelopes.
Second Order Backward Stochastic Difierential Equations and Fully Nonlinear Parabolic PDEs
TL;DR: In this article, the existence and uniqueness of adapted processes Y, Z, i and A solving the second order backward stochastic difierential equation (2BSDE) was studied.
Journal ArticleDOI
BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations
N. El-Karoui,S. Hamadène +1 more
TL;DR: In this article, the authors deal with the risk-sensitive control, zero-sum and non-zero-sum game problems of stochastic functional differential equations, and they show the existence of an optimal control and, a saddle-point and an equilibrium point for respectively the zero sum and non zero sum games.
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Adapted solution of a backward stochastic differential equation
TL;DR: In this paper, the authors considered the problem of finding an adapted pair of processes with values in Rd and Rd×k, respectively, which solves an equation of the form: x(t) + ∫ t 1 f(s, x(s), y(s)) ds + ∪ t 1 [g(m, x, s, g(m)) + y(m)] dW s = X.