Abstract: We considered the existence condition of solution for a class of stochastic Riccati equation. Based on the characteristics of the stochastic Riccati equation, we constructed a backward stochastic differential equation without constraints by using It formula. The solution of backward stochastic differential equations satisfied the algebraic constraints corresponding stochastic Riccati equation during the construction. Thus we gave the existence condition of the solution of the stochastic Riccati equation by using the relation of them.

Key words: backward stochastic differential equation, constraint condition, stochastic Riccati equation, stochastic linear quadratic optimal control