Adapted solution of a degenerate backward spde, with applications

Jin Ma and Jiongmin Yong

Stochastic Processes and their Applications, 1997, vol. 70, issue 1, 59-84

Abstract: In this paper we prove the existence and uniqueness, as well as the regularity, of the adapted solution to a class of degenerate linear backward stochastic partial differential equations (BSPDE) of parabolic type. We apply the results to a class of forward-backward stochastic differential equations (FBSDE) with random coefficients, and establish in a special case some explicit formulas among the solutions of FBSDEs and BSPDEs, including those involving Malliavin calculus. These relations lead to an adapted version of stochastic Feynman-Kac formula, as well as a stochastic Black-Scholes formula in mathematical finance.

Keywords: 60H15; 35R60; 34F05; 93E20; Degenerate; backward; stochastic; partial; differential; equations; Adapted; solutions; Forward-backward; stochastic; differential; equations; Malliavin; calculus; Feynman-Kac; formula; Option; pricing (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (12)

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