Behavior Analysis On Optimal Consumption And Portfolio In Financial Markets With Regime Switching

This thesis considers a consumption and investment problem where the market presents different regimes and the stocks pay dividends. An investor taking decisions continuously in time selects a consumption and investment strategy to maximize expected utility. Market factors and investor's utility of consumption depends on the regime of financial market. The market is modeled by an observable finite state continuous time Markov chain. In the case of stock dividend payments, the system can affect the prices of risk-free asset and risky assets. When the financial market switches between the different regimes, the influence of dividends on an investor's decision making is discussed.In this thesis, using stochastic differential equations and martingale method, the optimal consumption and portfolio is modeled. By the theories of Markov process and stochastic control, the verification theorem of the optimal policy is given. Also, with the dividend process and several special utility functions, the consumption and portfolio is explored by using verification theorem of an optimal policy, we obtain explicitly optimal consumption and investment strategies.Now suppose there are only two regimes in financial markets. The influence of the dividend payment on the optimal investment strategy is studied in this thesis. On financial markets with a regime switching, dividend policy will affect an investor's behavior. By several specific utility functions, the effect of dividends to an investor's consumption and investment is analyzed. After optimal consumption and investment strategies explicitly are given, they are discussed from the economic point of view.Based on different financial market regimes, the market will be divided into bull and bear markets. When we consider the payment of dividends, the optimal relative consumption in the bull market is higher than that with non-dividend, on the contrary, in a bear market, the optimal relative consumption is lower than that with non-dividend. These cases are consistent with the actual world. The case of the optimal investment strategy with regime switching has the theoretical and practical value.This thesis is arranged as follows. In Chapter 1, the background and objection of the thesis are introduced. In Chapter 2, we give a mathematical description of the consumption and portfolio problem with different regimes and the payment of dividends. In Chapter 3, by the theories of Markov process and stochastic control, the verification theorem of an optimal policy is given. In Chapter 4, from the verification theorem, the explicit optimal consumption and portfolio policies for specific HARA utility functions are obtained. Finally, the economic analysis for the market in two regimes switching is made for specific HARA utility functions and the potfolio strategy in the market with different regimes and payments of dividends are obtained.