On Study Of Optimal Investment With Inflation Under Nightian Uncertainty And Regime Switching

The optimal consumption and investment strategy problem is one of the basic problems of financial mathematics, receives extensive attention at home and abroad. The previous study of optimal investment and consumption is under the hypothesis of complete financial markets. In recent years, the re-searchers consider the influence of decision maker’s belief, Knightian uncer-tainty and regime-switching factors on investment strategy. The models of the investment strategy approaching economic realities are set up.We know that the Knightian uncertainty or ambiguity is not as same as risk. And the effects of Knightian uncertainty on investment strategy is signif-icant. In order to improve the investment model, we introduce Knightian un-certainty into the model. On the other hand, the regime-switching also has in-fluence on investment strategy. Through the analysis of the existing economic data, we find that inflation, random exchange rates and dividend payment also impact on investment strategy. Therefore, we will get a more meaningful in-vestment model by considering of Knightian uncertainty, regime-switching, inflation, random exchange rates and dividend payment on investment strate-gies.This paper studies the problem of optimal investment with inflation, ran-dom exchange rates and dividend payment under Knightian uncertainty and regime switching. Firstly, by using the Ito formula we obtain the dynamics of profit flow with regime switching. Secondly, a-maxmin expected utility (α-MEU) model is utilized to characterize an investor’s expected value of the investment. Thirdly, the profit flow calculation formula with random exchange rates are derived by the stochastic calculus, and the critical present values of the profit flow are also given. Finally, the numerical simulations are provided for explaining the effect of the parameters on an investor’s investment. By considering of the inflation, random exchange rates and dividend payment un- der Knightian uncertainty and regime switching environment we improve the existing investment model.