Variant reflected BSDE with application to finance
Abstract
The purpose of this thesis is to study a variance of reflected backward stochastic differential equation (VRBSDE) problem, where the reflection process A enters the drift in a non-linear manner to keep the solution process Y always above a given stochastic process X. Existence and Uniqueness theorems are proved by applying the fixed point argument and stochastic representation, introduced by Bank and El Karoui [2]. Comparison Theorem and continuous dependence theorem are also studied as the properties of VRBSDE. Given the recursive nature, the solution solves a recursive intertemporal utility minimization problem. The relationship between the equation and the optimal stopping problem is also presented as an application. American type claim pricing is discussed while the reflection A determines the early exercise signal, which extends the level crossing principle. A two-sided VRBSDE problem as well as its connection to the American Game option pricing are also proposed for future interests.
Degree
Ph.D.
Advisors
Ma, Purdue University.
Subject Area
Applied Mathematics|Mathematics|Finance
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