Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
Bruno Bouchard,Nizar Touzi +1 more
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TLDR
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.About:
This article is published in Stochastic Processes and their Applications.The article was published on 2004-06-01 and is currently open access. It has received 615 citations till now. The article focuses on the topics: Malliavin calculus & Stochastic differential equation.read more
Citations
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Applications of Malliavin calculus to Monte-Carlo methods in finance. II
TL;DR: This paper returns to the formulas developed in [1] concerning the “greeks” used in European options, and answers the question of optimal weight functional in the sense of minimal variance.
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A regression-based Monte Carlo method to solve backward stochastic differential equations
TL;DR: In this article, the numerical resolution of backward stochastic differential equations is studied and a new numerical scheme based on iterative regressions on function bases is proposed, which coefficients are evaluated using Monte Carlo simulations.
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A quantization algorithm for solving multidimensional discrete-time optimal stopping problems
Vlad Bally,Gilles Pagès +1 more
TL;DR: In this paper, a new grid method for computing the Snell envelope of a function of an approximate simulatable Markov chain (X_k) is proposed, which is a typical nonlinear problem that cannot be solved by the standard Monte Carlo method.
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Optimal multiple stopping and valuation of swing options
René Carmona,Nizar Touzi +1 more
TL;DR: In this paper, the authors investigated the mathematical generalization of these results to the case of possible multiple stopping and proved existence of the multiple exercise policies in a fairly general set-up.
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A forward scheme for backward SDEs
Christian Bender,Robert Denk +1 more
TL;DR: A forward scheme for simulating backward SDEs is introduced that avoids high order nestings of conditional expectations backwards in time and an implementable algorithm is presented and its convergence is proved.
References
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Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book
Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
Book
Numerical Solution of Stochastic Differential Equations
Peter E. Kloeden,Eckhard Platen +1 more
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
Book
The Malliavin Calculus and Related Topics
TL;DR: The Malliavin calculus as mentioned in this paper is an infinite-dimensional differential calculus on a Gaussian space, originally developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis.
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Valuing American Options by Simulation: A Simple Least-Squares Approach
TL;DR: In this paper, a new approach for approximating the value of American options by simulation is presented, using least squares to estimate the conditional expected payoff to the optionholder from continuation.