Reflected backward stochastic differential equations, convex risk measures and American options

Robert J. Elliott, Tak Kuen Siu

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We use convex risk measures to assess unhedged risks for American-style contingent claims in a continuous-time non-Markovian economy using reflected backward stochastic differential equations (RBSDEs). A two-stage approach is adopted to evaluate the risk. We formulate the evaluation problem as an optimal stopping-control problem and discuss the problem using reflected BSDEs. The convex risk measures are represented as solutions of RBSDEs. In the Markov case, we relate the RBSDE solutions to the unique viscosity solutions of related obstacle problems for parabolic partial differential equations.

Original languageEnglish
Pages (from-to)1077-1096
Number of pages20
JournalStochastic Analysis and Applications
Volume31
Issue number6
DOIs
Publication statusPublished - Nov 2013

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