A stochastic price model with random parameter is established in this paper. The stochastic price model with random parameter can be reduced to an equivalent deterministic model by orthogonal polynomial approximation. The deterministic linear stability, bifurcation theory and mathematics analysis method are applied to discuss the stability and bifurcation in the equivalent model. It is discovered that the parameter intervals for asymptotic stability in stochastic price model are related to the random parameter. The larger the random parameter is, the smaller the parameter interval for the asymptotic stability is. At the same time, it can be proved that Hopf bifurcation exists in stochastic price model. At last, theoretical results are supported by numerical simulations.

stochastic price model, orthogonal approximation, asymptotic stability, bifurcation.