Continuous-time Portfolio Selection

This paper introduces Mathematical Finance at first,and summarize conceptions and development,then generalize principal contents of Mathematical Finance:modern portfolio selection,CAPM,APT,Black-Scholes model and so on.Mathematical Finance is intersect of Mathematic and Finance,and introduces principal modern Mathematical methods of Mathematical Finance,and give a discription of principal theory and methods of Mathematical Finance: stochastic differential equation and stochastic optimal control.And then According to the definition of loss, this paper develops a new model of continuous-time portfolio selection and emphasizes to resolve the model by using the theory of stochastic optimal control.On the basis of the definition of the value function and the coefficient of risk aversion, the nonlinear transformation of value function is proved to satisfy HJB partial differential equation with the coefficent of risk aversion。Specially,optimal tactics of portfolio selection is proposed if the coefficient of risk aversion is infinite,Finally,an example is provided,and the problem is further discussed。In real life, investors are mostly partial to risk aversion just to have different degree. Therefore, studying behaviour of investors partial to risk aversion has important significance.