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Evaluation of the risk of automobile insurance with ruin theory

100%
Delong L.
Roczniki Kolegium Analiz Ekonomicznych
|
2005
|
vol. 14
27-44
EN
The paper considers the modified Sparre Andersen model which takes into account the ability of the insurer to invest its surplus in short-term assets. New derivation of the exponential upper bound for the ultimate ruin probability in this model (generalized Lundberg's inequality) is presented. The proof is based on the theory of supermartingales. As an application, the model is used to evaluate the risk of insolvency of a motor portfolio. A portfolio with a known structure of driver's claim propensity is considered in which drivers generate claims by compound Poisson processes with exponential severities. In numerical example, it is shown that the upper bound, derived for the modified Sparre Andersen model, can serve as an easy and quick indication of soundness of a portfolio. Sensitivity analysis of ruin probability is performed and its role in decision-making process of insurance company is discussed.
2

OPTIMAL STRATEGY FOR A DISCRETE RISK PROCESS IN CASE OF ORDERED CLAIM DISTRIBUTIONS

100%
Groniowska A.
Przegląd Statystyczny
|
2007
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vol. 54
|
issue 2
63-78
EN
The paper concerns the problem of choosing the optimal strategy by the insurer to minimalize the infinite time ruin probability. The authoress considers the risk process which is discrete with respect both to the time and the state space. She assumes that the insurer is able to change dynamically the portfolio content at every moment the risk process is observed. It means there is a possibility to change the parameters which influence the claim size distribution. A modification of the risk process allows to establishy that the optimal strategy exists and is obtained by comparing ruin probabilities for fixed claim size distributions. For stochastically ordered distributions it is possible to present the form of the optimal strategy. It consists in choosing always this distribution which is at least in the sense of this order. However, the same policy is not optimal for distributions ordered by the covex order. There are two counterexamples in the paper. The first one is analytical and concerns the easy case which one can call simple random walk, the second one is numerical but is more realistic. The optimal strategy for any discrete claim size distributions can be obtained numerically. Howeber, the results are not always consistent with intuitive expectations. t
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