Optimal Dividend Policy of Life Insurance Company under Quasi-hyperbolic Discounting

摘要

We discuss optimal dividend policy of life insurance companies assuming that customers have time inconsistent preferences. Dividend policy is given as the result of resolving the trade-off between the distribution and the investment; on one hand a company tries to pay a dividend as high as possible to appeal the customers. On the other hand, the company simultaneously tries to increase the amount of investment for future distribution of dividends. The both sides of decision-making must be reflected with the preference of the customers; more specifically their time preference. Recent evidence of psychological studies shows that people tend to choose alternatives in a time-inconsistent manner when making the inter-temporal decision. Together with the quasi-hyperbolic discounting, which can effectively explain this time inconsistent preference, we set up an optimization problem of customers' utility for dividends in order to determine the optimal dividend policy of insurance companies. We solve the optimization problem in maximizing the discounted utilities of multi-agents with backward induction. Additionally to see the effect of the psychological factor, we compare the optimal dividend policy implied by time-inconsistent preference with time-consistent one.