Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematically-inclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious...

Optimal forms of reinsurance policies have been studied for a long time in actuarial literature. Most existing results are from the insurer's point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is...

Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematically-inclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious...

To assess the required capital for insurance companies, which usually have several business lines, estimates of the joint tail probabilities of aggregate losses are needed. Under the collective risk model, these aggregate losses are sums of random number of random variables, whose distributions...