A BSDE approach to convex risk measures for derivative securities

Robert J. Elliott, Tak Kuen Siu

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)1083-1101
Number of pages19
JournalStochastic Analysis and Applications
Issue number6
Publication statusPublished - Nov 2012


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