Continuity problem for backward stochastic differential equations with singular nonmarkovian terminal conditions and random terminal times

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Sharoy Samuel PhD Thesis .pdf

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2021-7

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Samuel, Sharoy Augustine

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We study a class of nonlinear BSDEs with a superlinear driver process f adapted to a filtration F and over a random time interval [0, S] where S is a stopping time of F. The filtration is assumed to support at least a d-dimensional Brownian motion as well as a Poisson random measure. The terminal condition ξ is allowed to take the value +∞, i.e., singular. Our goal is to show existence of solutions to the BSDE in this setting. We will do so by proving that the minimal supersolution to the BSDE is a so lution, i.e., attains the terminal values with probability 1. We focus on non-Markovian terminal conditions of the following form: 1) ξ1 = ∞·1{τ≤S} and 2) ξ2 = ∞·1{τ>S} where τ is another stopping time. We call a stopping time S solvable with respect to a given BSDE and filtration if the BSDE has a minimal supersolution with terminal value ∞ at terminal time S. The concept of solvability plays a key role in many of the arguments. We also use the solvability concept to relax integribility conditions assumed in previous works for continuity results for BSDE with singular terminal conditions for terminal values of the form ∞ · 1{τ≤T} where T is deterministic. We provide numerical examples in cases where the solution is explicitly computable and a basic application in optimal liquidation.

Subject Keywords

BSDE in Finanance, Non Markovian Singular Terminal Value, Control Problem, Continuity Problem

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https://hdl.handle.net/11511/91536

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

S. A. Samuel, “Continuity problem for backward stochastic differential equations with singular nonmarkovian terminal conditions and random terminal times,” Ph.D. - Doctoral Program, Middle East Technical University, 2021.