Optimal Consumption And Investment Policy, With Interest Rates And Taxes

In this thesis, we study the optimal investment and consumption problem in which tax and interest are concerned. By using the dynamic programming method in stochastic optimal control theory, the corresponding optimal investment and consumption strategies in the sense of maximizing the related utility functions are obtained.In chapter 3, the optimization problem on investment policy is considered when tax is taken into account and the interest rate of risk-free asset is random. The associated optimal investment policy which maximizing the expectation of exponential utility function is obtained, and the relations between the optimal investment policy and various parameters are shown by numerical calculation.In chapter 4, consumption and investment are simultaneously considered under the same conditions on tax and interest rate as in chapter 3. By applying the stochastic dynamic programming method and duality theory, the optimal consumption and investment strategy is obtained. As is showed in the end of this chapter, the conclusions for the classical Merton model can be regarded as a special case of our results here.In the final chapter, we study the jump- diffusion risk model with consumption and investment, where tax, dividend and interest are concerned at the same time. The interest in this chapter is assumed to be a constant. Similar conclusions to the previous two chapters are obtained when the utility function is substituted by a power utility function.