Suchergebnisse

This book provides an overview of classical actuarial techniques, including material that is not readily accessible elsewhere such as the Ammeter risk model and the Markov-modulated risk model. Other topics covered include utility theory, credibility theory, claims reserving and ruin theory. The author treats both theoretical and practical aspects and also discusses links to Solvency II. Written by one of the leading experts in the field, these lecture notes serve as a valuable introduction to some of the most frequently used methods in non-life insurance. They will be of particular interest to graduate students, researchers and practitioners in insurance, finance and risk management

AbstractWe consider a risk model in discrete time with dividends and capital injections. The goal is to maximise the value of a dividend strategy. We show that the optimal strategy is of barrier type. That is, all capital above a certain threshold is paid as dividend. A second problem adds tax to the dividends but an injection leads to an exemption from tax. We show that the value function fulfils a Bellman equation. As a special case, we consider the case of premia of size one. In this case we show that the optimal strategy is a two barrier strategy. That is, there is a barrier if a next dividend of size one can be paid without tax and a barrier if the next dividend of size one will be taxed. In both models, we illustrate the findings by de Finetti's example.

AbstractWe consider a Cramér–Lundberg model representing the surplus of an insurance company under a general reinsurance control process. We aim to minimise the expected time during which the surplus is bounded away from its own running maximum by at least $$d>0$$

d
>
0

(discounted at a preference rate $$\delta >0$$

δ
>
0

) by choosing a reinsurance strategy. By analysing the drawdown process (i.e. the absolute distance of the controlled surplus model to its maximum) directly, we prove that the value function fulfils the corresponding Hamilton–Jacobi–Bellman equation and show how one can calculate the value function and the optimal strategy. If the initial drawdown is critically large, the problem corresponds to the maximisation of the Laplace transform of a passage time. We show that a constant retention level is optimal. If the drawdown is smaller than d, the problem can be expressed as an element of a set of Gerber–Shiu optimisation problems. We show how these problems can be solved and that the optimal strategy is of feedback form. We illustrate the theory by examples of the cases of light and heavy tailed claims.