The Optimal Model Of Security Investment Portfolio

In the study fina ncia l mathematics, it is a important aspect that usethe theory of the stochastic control to study the tactics of optima linvestment .In the non-rub fina nce market,there are ma ny literature toresearch for investment tactics ,and they have got some good conclusions.With the developing of the fina ncia l mathematics, the study of investmenttactics becomes hot spots in the rub market. By considering the dividendand tax acting to the establishment of fina nce market and the option of thetactics of investment and other problems, it is of powerful practica lsignifica nce, at the same time the study of problem becomes more difficulttoo. This paper researches the optima l investment tactics of two fina ncia lrisk models. In the first model we suppose that there is a fina nce market inwhich n risk securities and a bond are traded continuously; the risksecurities have been paid the tax and continuous dividends .An investorwhose total initia l wealth is invested in two securities using averse the riskutility function. Through controlling alloca tion rate of investment in twosecurities, the investor expected ma xima l wealth utility value at termina l.While state varia nces are complicated information, which propose riskavers ion coefficient, we have got the tactics of optima l feedback. Further,we analyze the solution of the two risk averse functions of optima l feedback controlling under the conditions of at the extremely abhor risk.An example was provided. In the second model, optima l investmentportfolio and consumption policies with two stocks are studied. First of all,the stochastic model in the fina ncia l market was introduced. By using Itoformula, the stochastic differential equation for fortune that was concernedwith the decision of consumption and investment was given; the stochasticcontrol model for consumption and investment was established. By usingthe dynamica l programming method, the optima l investment portfolio andconsumption policies for one kind of typica l utility function case areobtained,then we make numerica l simulation for it and get the numerica lsolution.