A Note on Indefinite Stochastic Riccati Equations
Probability
2012-03-20 v1
Abstract
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 BSDEs (without involving any algebraic constraint) whose existence of solutions automatically enforces the original algebraic constraint to be satisfied.
Keywords
Cite
@article{arxiv.1203.3857,
title = {A Note on Indefinite Stochastic Riccati Equations},
author = {Zhongmin Qian and Xun Yu Zhou},
journal= {arXiv preprint arXiv:1203.3857},
year = {2012}
}