One Kind Of International Optimal Security Investment Problem Under The Partial Information

The international portfolio diversification depends on several factors, such as the different expected rates of return, the paying dividends of the securities, the volatilities, the regulations and transaction costs in different countries, depends on the effect of exchange risks and so on. We have many theories of expected utility maximization, but only about full information case. That is to say, the drift term need to be observable. Obviously, it is not practical. Because the investor grasps not the natural filtration {F_t}_{0≤t≤T} generated by W_t, but the filtration {Z_t}_{0≤t≤T}, generated by the price process. So only {Z_t}_{0≤t≤T} adaptive processes are observable.In this paper, we mainly discuss one kind of international optimal security investment portfolio and consumption choice problem under the partial information, so as to the analysis of correlation of the parameters.This paper consists of four chapters.In Chapter 1, we introduce the mathematical model of international security investment between two countries. Meanwhile, we retrospect to some existing results.In Chapter 2, we present nonlinear filtration theory, and find out the nonlinear conditional Gaussian filtering estimation under one dim and multi dims.In Chapter 3, we transfer the problem under the partial information to a case under the full information using the nonlinear filtering estimation. Then we induce the problem of the maximization of utility and get the optimal solution by HJB function.