Reflected solutions of backward SDE's, and related obstacle problems for PDE's
TLDR
In this article, reflected solutions of one-dimensional backward stochastic differential equations are studied and the authors prove uniqueness and existence both by a fixed point argument and by approximation via penalization.Citations
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Journal ArticleDOI
Backward Stochastic Differential Equations in Finance
TL;DR: In this article, different properties of backward stochastic differential equations and their applications to finance are discussed. But the main focus of this paper is on the theory of contingent claim valuation, especially cases with constraints.
Journal ArticleDOI
Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
Bruno Bouchard,Nizar Touzi +1 more
TL;DR: In this paper, a discrete-time approximation for decoupled forward-backward stochastic dierential equations is proposed, and the L p norm of the error is shown to be of the order of the time step.
Journal ArticleDOI
Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type
TL;DR: In this article, the authors obtained the following limit theorem: if a sequence of RCLL supersolutions of a backward stochastic differential equations (BSDE) converges monotonically up to (y, z) with E[sup t istg |y� t istg ] < ∞, then the supersolution itself is a RCLL of the same BSDE (Theorem 2.4 and 3.6).
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
Backward stochastic differential equations with reflection and Dynkin games
Jakša Cvitanić,Ioannis Karatzas +1 more
TL;DR: 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.
References
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Book
Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.
Journal ArticleDOI
User’s guide to viscosity solutions of second order partial differential equations
TL;DR: The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorem, and continuous dependence may now be proved by very efficient and striking arguments as discussed by the authors.
Journal ArticleDOI
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.
Journal ArticleDOI
Backward Stochastic Differential Equations in Finance
TL;DR: In this article, different properties of backward stochastic differential equations and their applications to finance are discussed. But the main focus of this paper is on the theory of contingent claim valuation, especially cases with constraints.
Journal ArticleDOI
Stochastic differential utility
TL;DR: In this article, a stochastic differential formulation of recursive utility is given sufficient conditions for existence, uniqueness, time consistency, monotonicity, continuity, risk aversion, concavity, and other properties.
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Adapted solution of a backward stochastic differential equation
Backward stochastic differential equations and quasilinear parabolic partial differential equations
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