Bayesian Ideas for Premium Strategies

The traditional control parameters in determining the strategy of an insurance company are dividends and reinsurance arrangements. Premiums are obviously of equal practical importance, but theoretical studies are rarer. We use here the traditional Bayesian view of the risk parameters of the insured (say the Poisson rate of generating car accidents) to be randomly fluctuating in the portfolio. This allows quantifying the influence of the premium level on the portfolio size and thereby approaching control problems such as minimizing the ruin probability. Also deductibles are in part involved. Further a game theoretic perspective via differential games in a competitive market is outlined.