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Stochastic Control Representations for Penalized Backward Stochastic Differential Equations

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)1440–1463.
Number of pages24
JournalSIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume53
Issue number3
DOIs
Publication statusPublished - 2015

Documents

  • 1302.0480v5

    1302.0480v5.pdf, 327 KB, application/pdf

    12/06/2015

    Accepted author manuscript

King's Authors

Abstract

This paper shows that penalized backward stochastic differential equation (BSDE), which is often used to approximate and solve the corresponding reflected BSDE, admits both optimal stopping representation and optimal control representation. The new feature of the optimal stopping representation is that the player is allowed to stop at exogenous Poisson arrival times. The convergence rate of the penalized BSDE then follows from the optimal stopping representation. The paper then applies to two classes of equations, namely multidimensional reflected BSDE and reflected BSDE with a constraint on the hedging part, and gives stochastic control representations for their corresponding penalized equations.

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