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Ruin Probabilities in a Finite-Horizon Risk Model with Investment and Reinsurance

Part of: Markov processes Mathematical economics Stochastic systems and control

Published online by Cambridge University Press:  30 January 2018

R. Romera  and
W. Runggaldier
R. Romera*
Affiliation:
University Carlos III de Madrid
W. Runggaldier*
Affiliation:
University of Padova
*
∗ Postal address: Department of Statistics, Universidad Carlos III de Madrid, c/Madrid 126, 28903, Getafe, Madrid, Spain. Email address: rosario.romera@uc3m.es
∗∗ Postal address: Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121 Padova, Italy.
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Abstract

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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.

Keywords

Risk processsemi-Markov processoptimal reinsurance and investmentLundberg-type bound

MSC classification

Primary: 91B30: Risk theory, insurance 93E20: Optimal stochastic control 60J28: Applications of continuous-time Markov processes on discrete state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 954 - 966
Copyright
© Applied Probability Trust 

Footnotes

Partially supported by the Spanish ME grant SEJ2007-64500. Part of the contribution by this author was obtained while he was visiting professor 2009 for the chair Quantitative Finance and Insurance at the LMU University in Munich funded by LMU Excellent. Hospitality and financial support are gratefully acknowledged.

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