A Study On The Optimal Investment And Consumption Model Based On Habit Formation In Preferences

As one of the most fundamental problems of financial mathematics, the study of optimal investment and consumption has always been a concerning problem.In this paper, it was our main work to study the optimal investment and consumption model based on habit formation. At first, the growth optimal wealth model was established by direct construction method in fixed time horizon [0,T], and the optimal investment strategy was also obtained. Then, considering the variability of market factor and the other factors, investors could not fix their time horizons when the investment choices were made, so we further considered the optimal investment and consumption problem to fit the finance practice when time horizon was uncertain in finite financial time interval[0,T], and the same optimal investment strategy was obtained when time horizon was fixed or uncertain. What's more, the optimal investment and consumption problem including financial derivatives as investment tools was researched, and some new theoretical and practical results of finance were concluded. Contrast to the traditional optimal investment and consumption problem, we introduced the optimal investment and consumption problem based on habit formation, which greatly enriched the research results. At last, we studied optimal consumption,life insurance and risk investment rules for a wage earner whose life-time was random based on habit formation in preferences, and inferred the optimal admissible strategy pair for usual utility function. For the instantaneous utility function being power-linear and the specific CRRA case for legacy and terminal utility, we got the explicit rules of optimal consumption and life insurance and risk investment.