Introduction

The principal tasks in general insurance are solvency and pricing. Solvency is the financial control of liabilities under nearly worst-case scenarios. The target is the so-called reserve; i.e., the upper percentiles qε of the portfolio liability X. Modelling was reviewed in the preceding chapters, and the issue now is computation. We may need the entire distribution of X, and Monte Carlo is the obvious general tool. Some problems can be handled by simpler Gaussian approximations, possibly with a correction for skewness added. Computational methods for solvency are discussed in the next two sections.

The second main topic is the pricing of risk. This has a market side. A company will gladly charge what people are willing to pay! Yet a core is the pure premium π = E(X) or Π = E(X); i.e., the expected policy or portfolio payout during a certain period of time. Evaluations of these are important not only as a basis for pricing, but also as an aid to decision-making. Not all risks are worth taking! Pricing or rating methods follow two main lines. One of them draws on claim histories of individuals. Those with good records are considered lower risk and rewarded (premium reduced), those with bad records are punished (premium raised). The traditional approach is through the theory of credibility, a classic presented in Section 10.5. Price differentials can also be administered according to the experience with groups.