Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values

Date

2017-08-03

Author

Sezer, Ali Devin
Popıer, Alexandre

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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 ξ = ∞ · 1B(m,r) c (for which q > 2 is assumed) or ξ = ∞ · 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.

URI

https://hdl.handle.net/11511/77317

Conference Name

Workshop on Stochastic processes - Actuarial science and Finance

Collections

Graduate School of Applied Mathematics, Conference / Seminar

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Citation Formats

A. D. Sezer and A. Popıer, “Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values,” presented at the Workshop on Stochastic processes - Actuarial science and Finance, 2017, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/77317.