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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}
}
R2 v1 2026-06-21T20:35:34.997Z