A BSDE approach to convex risk measures for derivative securities

Robert J. Elliott; Tak Kuen Siu

doi:10.1080/07362994.2012.727141

A BSDE approach to convex risk measures for derivative securities

Robert J. Elliott, Tak Kuen Siu

Department of Applied Finance

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

4 Citations (Scopus)

Abstract

A backward stochastic differential equation (BSDE) approach is used to evaluate convex risk measures for unhedged positions of derivative securities in a continuous-time economy. The convex risk measure is represented as the solution of a BSDE. We use the Clark-Ocone representation result together with Malliavin calculus to identify the integrand in the martingale representation associated with the BSDE. In the Markov case, we relate the BSDE solution to a partial differential equation solution for convex risk measure evaluation.

Original language	English
Pages (from-to)	1083-1101
Number of pages	19
Journal	Stochastic Analysis and Applications
Volume	30
Issue number	6
DOIs	https://doi.org/10.1080/07362994.2012.727141
Publication status	Published - Nov 2012

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10.1080/07362994.2012.727141

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A BSDE approach to convex risk measures for derivative securities

Abstract

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