Description: This paper investigates the optimal multi-period proportional reinsurance strategy that minimizes the ruin probability of an insurer. Some conditions under which it is optimal to have no reinsurance are derived. Based on these results, a new concept, capital threshold of proportional reinsurance, is introduced. In the case of two periods, a lower bound of the capital threshold of proportional reinsurance is provided. Some economic implications and properties of this new concept are also discussed.

Description: In this paper we investigate three investment-consumption problems for a risk averse investor: i an investment only problem that involves utility from only terminal wealth, ii an investment-consumption problem that involves utility from only consumption, and iii an extended investment-consumption problem that involves utility from both consumption and terminal wealth. We model these problems under a multiperiod setup that incorporates three types of uncertainties: the economic environment uncertainty, the asset return uncertainty, and the mortality uncertainty. By using dynamic programming, analytical expressions of the optimal investment consumption strategies to these problems are derived. Some economic implications on these results are also discussed.