Research On The Specific Financial Derivative Pricing And Portfolio Models

Continuous time portfolio optimization and financial asset pricing problem is an important research content in the mathematical finance and financial mathematics. The pricing of financial assets is a research on the reasonable pricing of financial derivatives, continuous time portfolio is also important theory and methodology for investors and investment institutions in the asset and risk hedge strategy. In this paper, we study the problem of financial asset pricing and investment portfolio. This article discusses the problems of financial asset pricing and continuous time investment portfolio in financial markets.Study on the call option pricing model under the nonlinear dynamic. Based on Black-Scholes option pricing theory, the classic option pricing theory assumes that the holder is not trading in the stock option within the validity period. In this paper, we consider the option holder after the call option may be traded within the validity period of the option of investment strategy. Assuming the according to the investment strategy of nonlinear hold shares, we have obtained the pricing formulas, The improved option pricing formula under the appropriate conditions for the degradation of the classical pricing formula.Study on the optimal investment strategy of the portfolio under the quadratic utility. We research the optimal investment strategy for portfolio quadratic utility. Under the expected utility maximization criterion, the dynamic programming principle is used to obtain the HJB equation for the value function, and we study the optimal investment strategies under quadratic utility. Finally, we obtain the explicit solutions for the optimal investment strategies.