We consider the problem of finding optimal dynamic premium policies in non-life insurance. The company controls dynamically the relative safety loading with the possibility of gaining or loosing customers. It distributes dividends according to a 'barrier strategy' and the objective of the company is to find an optimal premium policy and dividend barrier maximizing the expected total, discounted pay-out of dividends. In the case of exponential claim size distributions optimal controls are found on closed form, while for general claim size distributions a numerical scheme for approximations of the optimal control is derived. Based on the idea of De Vylder going back to the 70ths,we also investigate the possibilities of approximating the optimal control in the general case by using the closed form solution of an approximating problem with exponential claim size distributions.
Special attention is paid to sequences of independent random variables having finite variances.
Some results will be presented concerning sequences of arbitrary random variables without any assumptions about the existence of moments. We investigate the interaction between optimal portfolio choice and fair pricing of specific insurance contracts. In particular, we consider so-called participating policies. We find fair contract specifications in the sense that the market values of future claims to policy holders and equity holders, respectively, are equal to their initial deposits. We motivate that the manager should optimize utility of final wealth for the policy holders and find closed form solutions for the optimal solutions.