Optimal consumption, investment and insurance strategy applications

Drawing on the existing literature, a utility-maximising agent is studied in the application of a life-cycle optimal strategy of consumption, investment and insurance to different, and unexplored, scenarios. Key factors, including time inconsistent preferences, an optimal stopping time and a dynamic risk environment,can affect agents' behaviour and thereby influence their financial strategies .In this thesis three research papers are developed to apply optimal strategies in various circumstances. In the first research paper, an optimal portfolio management model with hyperbolic discounting and luxury-type bequest motives is used to explain the annuity puzzle - the low demand for voluntary life annuities. Using hyperbolic discounting, agents' time-inconsistent preferences can be described and measured in the model. Two extreme types of agents' time-inconsistent behaviours, "naïve" behaviour and "sophisticated" behaviour, are then examined and studied. To build a more realistic model, the luxury-type bequest motives are further incorporated into the model. The model in paper 1 is calibrated to Swiss data to obtain numerical results. In the second research paper, the financial planning problem of a retiree seeking to enter a retirement village at a future time is studied. As the retiree is assumed to be utility-driven and would fully annuitise her wealth at the time of entry, her optimal strategy is a solution to problems of both optimal control and optimal stopping. Within the context of dynamic health states, the optimal strategy should include an optimal plan of consumption, investment, bequest and insurance prior to the entry date, and an optimal stopping time to conduct the full annuitisation for entering the retirement village. For a case that has an initial deposit requirement for entering the retirement village, the optimal solution incorporates an American option replication. The model in paper 2 uses Australian data to present our numerical results In the final research paper, an optimal strategy is applied in a dynamic risk environment. Jumps and regime switching are incorporated in the risky asset diffusion to describe the dynamic risk environment. By extending the model in Richard (1975), a system of paired Hamilton-Jacobi-Bellman (HJB) equations is obtained and solved. Using numerical methods and calibrating to American data, the numerical results of agents' behaviours for different risk environments are obtained.