Existence of solutions to a class of indefinite stochastic Riccati equations

Journal article

An indefinite stochastic Riccati equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of such equations (including the existence of solutions) driven by one-dimensional Brownian motion. The idea is to replace the original equation by a system of backward stochastic differential equations (without involving any algebraic constraint) whose existence of solutions automatically enforces the original algebraic constraint to be satisfied. © 2013 Society for Industrial and Applied Mathematics.

Authors: Qian, Z; Zhou, X

• Journal: SIAM Journal on Control and Optimization
• Volume: 51
• Issue: 1
• Pages: 221-229
• Publication date: 2013-01-01
• DOI: 10.1137/120873777
• EISSN: 1095-7138
• ISSN: 0363-0129
• Language: English
• Keywords: Backward stochastic differential equation; Stochastic Riccati equation; Stochastic differential equation