Special Session 129: Qualitative and Quantitative Techniques for Differential Equations arising in Economics, Finance and Natural Sciences
Contents
Let {X_k} be strictly stationary sequence of d-dimensional centered random vectors satisfying the strong mixing condition. Consider a stochastic difference equation
DP(t_k)=P(t_k-1)(bt/n+s(t/n)^1/2 X_k),
where s is the volatility and b is the trend. It is known that the solution of this difference equation converges almost surely to a Black-Sholes type model Z(t). The purpose of this talk is to estimate an approximation of a stock price model Z(t) with a random volatility using P(t) and consider optimal portfolios for Z(t).