Adaptive control strategies and dependence of finite time ruin on the premium loading

The paper is devoted to risk theory insight into the problem of asset-liability and solvency adaptive management. Two adaptive control strategies in the multiperiodic insurance risk model composed of chained classical risk models are introduced and their performance in terms of probability of ruin is examined. The analysis is based on an explicit expression of the probability of ruin within finite time in terms of Bessel functions. The dependence of that probability on the premium loading, either positive or negative, is a basic technical result of independent interest.