Markovian forward-backward stochastic differential equations and stochastic flows

Robert J. Elliott; Tak Kuen Siu

doi:10.1016/j.sysconle.2012.04.013

Markovian forward-backward stochastic differential equations and stochastic flows

Robert J. Elliott^*, Tak Kuen Siu

^*Corresponding author for this work

Department of Applied Finance

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Markovian forward-backward stochastic differential equations, (MFBSDEs), are discussed by exploiting techniques of stochastic flows. Using martingale representation, a differentiation rule, stochastic flows of diffeomorphisms and the unique decomposition of special semimartingales, we identify the solution of the backward system of the FBSDE. Applications of the result to convex risk measures are discussed.

Original language	English
Pages (from-to)	1017-1022
Number of pages	6
Journal	Systems and Control Letters
Volume	61
Issue number	10
DOIs	https://doi.org/10.1016/j.sysconle.2012.04.013
Publication status	Published - Oct 2012

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10.1016/j.sysconle.2012.04.013

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title = "Markovian forward-backward stochastic differential equations and stochastic flows",

abstract = "Markovian forward-backward stochastic differential equations, (MFBSDEs), are discussed by exploiting techniques of stochastic flows. Using martingale representation, a differentiation rule, stochastic flows of diffeomorphisms and the unique decomposition of special semimartingales, we identify the solution of the backward system of the FBSDE. Applications of the result to convex risk measures are discussed.",

author = "Elliott, {Robert J.} and Siu, {Tak Kuen}",

year = "2012",

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doi = "10.1016/j.sysconle.2012.04.013",

language = "English",

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AU - Elliott, Robert J.

AU - Siu, Tak Kuen

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N2 - Markovian forward-backward stochastic differential equations, (MFBSDEs), are discussed by exploiting techniques of stochastic flows. Using martingale representation, a differentiation rule, stochastic flows of diffeomorphisms and the unique decomposition of special semimartingales, we identify the solution of the backward system of the FBSDE. Applications of the result to convex risk measures are discussed.

AB - Markovian forward-backward stochastic differential equations, (MFBSDEs), are discussed by exploiting techniques of stochastic flows. Using martingale representation, a differentiation rule, stochastic flows of diffeomorphisms and the unique decomposition of special semimartingales, we identify the solution of the backward system of the FBSDE. Applications of the result to convex risk measures are discussed.

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U2 - 10.1016/j.sysconle.2012.04.013

DO - 10.1016/j.sysconle.2012.04.013

M3 - Article

AN - SCOPUS:84865623847

SN - 0167-6911

VL - 61

SP - 1017

EP - 1022

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 10

ER -

Markovian forward-backward stochastic differential equations and stochastic flows

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