Backward stochastic differential equations with non-Markovian singular terminal values


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SEZER A. D. , Kruse T., Popier A.

STOCHASTICS AND DYNAMICS, vol.19, no.2, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1142/s0219493719500060
  • Journal Name: STOCHASTICS AND DYNAMICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Keywords: Backward stochastic differential equations, reaction-diffusion equations, singularity, non-Markovian terminal conditions, BSDES, BOUNDARY, TRACE

Abstract

We solve a class of BSDE with a power function f (y) = y(q), q > 1, driving its drift and with the terminal boundary condition xi = infinity . 1( B(m,r)c )(for which q > 2 is assumed) or xi = infinity . 1B(m,r), where B(m, r) is the ball in the path space C([0,T]) of the underlying Brownian motion centered at the constant function m and radius r. The solution involves the derivation and solution of a related heat equation in which f serves as a reaction term and which is accompanied by singular and discontinuous Dirichlet boundary conditions. Although the solution of the heat equation is discontinuous at the corners of the domain, the BSDE has continuous sample paths with the prescribed terminal value.