The Research Of Optimal Portfolio Models Under Disordered Asset Return And Partial Information

Financial market is a complex system, the asset return of the risky as-sets and investment risk are time-changed. The portfolio model still needs to be improved in the financial market, although many scholars in the field of portfolio have been fruitful research results. This paper studies the portfolio model which is based on the theory of semi-martingale, and applies the idea of disorder problem to characterizing the asset return of an investor which is pathological and has nothing from something, when the financial market is shocked by major events at a random moment. The core problem in this paper is how to hedge the contingent claim and to maximize the expected exponential utility of the terminal net wealth under partial information. The main results are as follows.Firstly, the research background and practical significance of the portfo-lio with asset return being disordered under partial information are introduced. The development has been reviewed in three aspects of the portfolio field. The first one is partial information, next one is interest rate and dividend paymen-t, the last one is that differentiating ambiguity and risk; and then the paper elaborates the content of research and gives the framework of research ideas.Secondly, interest rate which is the objective existence factor of the finan-cial market, is introduced in the model of the asset return being disordered. We provide the optimal strategy which can hedge the random payoff, as well as to maximize the expected exponential utility of the net wealth at terminal time, as the asset return process is available, and disorder moment and Brow-nian motion can not be observed. In details, first of all, the discounted asset price process is defined. Next, by applying stochastic differential equation, the posterior probability of the disorder time is characterized. From the theo-ry of semi-martingales and backward stochastic differential equation, we give and prove the expression of the value process and the optimal trading strategy under some conditions. At last, for an investor with exponential utility, the explicit expression of the value process and the optimal trading strategy are given by using It^o lemma and Girsanov’s changes.Thirdly, under partial information we use a model of the a-Maxmin ex-pected utility (α-MEU), differentiating ambiguity and ambiguity attitude of an investor, and study the problem of portfolio when the financial market with the asset return being disordered has non-zero interest rate. In fact, we first use the backward stochastic differential equation to characterize α-MEU. Next, giving the posterior probability process of disorder moment to satisfy a stochastic d-ifferential equation, we show that the value process is a unique solution of a backward stochastic differential equation. Further, by the techniques of mar-tingales, we work out the explicit expressions of optimal trading strategy as well as of value process in the particular case of exponential utility. Compar-ing Knight uncertainty with the general framework of the optimal investment strategy, we give the relationship and difference between them, and the expla-nations of corresponding economic are given.Finally, the results of this paper are summarized and the further researches in the portfolio model are provided in future.