By considering different filtrations for the pure insurance risk, we arrive at simple upper and lower bounds for the fair premiums. These bounds seem particular relevant for the valuation of reinsurance contracts, since reinsurers often receive only scarce information after the selling of the contracts. As the exact value of the local Lundberg coefficient can be found for only simple claim size distributions we propose to use an approximation of this coefficient. Also we investigate the case where the premium rate is piecewise linear. And we propose an approach to simulate risk processes with reserve dependent claims which, in particular, covers the case of mixed Poisson premium rate or the reserve depending on stock price changes.
Special attention is given to comparison of simulation time and accuracy.
Optimal is meant in the sense of minimizing the ruin probability. Two basic examples are discussed. In this talk, conditions for optional stopping of the Kella-Whitt martingale are discussed, a Markov additive extension is presented and applications to a variety of problems are outlined. Joint work with Offer Kella, Jerusalem. At each moment of time the management of the company makes a decision of the amount of dividends paid-out to the shareholders.