Journal of Applied Probability

Ruin probabilities in a finite-horizon risk model with investment and reinsurance

R. Romera and W. Runggaldier

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A finite-horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Our setting is innovative in the sense that we describe in a unified way the timing of the events, that is, the arrivals of claims and the changes of the prices in the financial market, by means of a continuous-time semi-Markov process which appears to be more realistic than, say, classical diffusion-based models. Obtaining explicit optimal solutions for the minimizing ruin probability is a difficult task. Therefore we derive a specific methodology, based on recursive relations for the ruin probability, to obtain a reinsurance and investment policy that minimizes an exponential bound (Lundberg-type bound) on the ruin probability.

Article information

J. Appl. Probab., Volume 49, Number 4 (2012), 954-966.

First available in Project Euclid: 5 December 2012

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Zentralblatt MATH identifier

Primary: 91B30: Risk theory, insurance 93E20: Optimal stochastic control 60J28: Applications of continuous-time Markov processes on discrete state spaces

Risk process semi-Markov process optimal reinsurance and investment Lundberg-type bound


Romera, R.; Runggaldier, W. Ruin probabilities in a finite-horizon risk model with investment and reinsurance. J. Appl. Probab. 49 (2012), no. 4, 954--966. doi:10.1239/jap/1354716650.

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