Optimal Consumption-Portfolio And Retirement Problem

The optimal consumption-portfolio problem has been a basic one in mathematical finance, has also been researched by many scholars at home and abroad. In this paper, combined the investors’ optimal consumption-portfolio with retirement, under some different borrowing constraints for the investors, the decision making problems are discussed. Finally, the Knight uncertainty being included in the model, the optimal strategies are further investigated.Firstly, this paper explores consumption-investment and leisure choices in a life-cycle model with habit formation, stochastic opportunity set, stochastic wages and labor supply flexibility. In the case of stock dividend payments, the asset model is established by using stochastic differential equations. The investors’preferences are represented by the no separable von Neumann Morgenstern index. Finally, the explicit expressions of optimal choices are obtained for optimal consumption-portfolio and leisure.Secondly, this paper studies the consumption-investment and leisure choices with the investor’s heritage and insurance in which the dividend repayment of the stock and three different borrowing constraints are considered. The optimal consumption-investment and bequest of investors has been solved in explicit expressions by using the stochastic differential equations and the martingale method. Based on numerical analysis, both the investment and consumption ratios have been explored in the three different situations. The effect of the dividends on an investor’s investment and consumption has also been analyzed.Finally, this paper investigates an optimal consumption and portfolio problem with an investor’s heritage and insurance under Knight uncertainty and three different borrowing constraints. The optimal consumption-investment and bequest of an investor have been solved explicitly by using the backward stochastic differential equations (BSDEs) theory. And, numerical results show that both ambiguity and ambiguity attitude affect the optimal consumption and portfolio choices.