Description: It is obvious that the introduction of a deductible has two major effects. The amount paid for every claim will drop, resulting in a lower claim burden for the insurance company. There will also be a drop in claim frequency, leading to a decrease in claim handling expenses. However, it is by no means obvious how the average claim size changes with the introduction of a deductible. In this paper, we will study this question. First, we derive some theoretical results then apply them to concrete distributions.

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.