Journal of Applied Probability

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

R. Romera and W. Runggaldier

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 5 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1354716650

Digital Object Identifier
doi:10.1239/jap/1354716650

Mathematical Reviews number (MathSciNet)
MR3058981

Zentralblatt MATH identifier
1255.91185

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

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

Citation

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. https://projecteuclid.org/euclid.jap/1354716650


Export citation

References

  • Asmussen, S. (2000). Ruin Probabilities. World Scientific, River Edge, NJ.
  • Chen, S., Gerber, H. U. and Shiu, E. S. W. (2000). Discounted probabilities of ruin in the compound binomial model. Insurance Math. Econom. 26, 239–250.
  • Diasparra, M. A. and Romera, R. (2009). Bounds for the ruin probability of a discrete-time risk process. J. Appl. Prob. 46, 99–112.
  • Diasparra, M. and Romera, R. (2010). Inequalities for the ruin probability in a controlled discrete-time risk process. Europ. J. Operat. Res. 204, 496–504.
  • Edoli, E. and Runggaldier, W. J. (2010). On optimal investment in a reinsurance context with a point process market model. Insurance Math. Econom. 47, 315–326.
  • Eisenberg, J. and Schmidli, H. (2011). Minimising expected discounted capital injections by reinsurance in a classical risk model. Scand. Actuarial J. 2011, 155–176.
  • Gaier, J., Grandits, P. and Schachermayer, W. (2003). Asymptotic ruin probabilitites and optimal investment. Ann. Appl. Prob. 13, 1054–1076.
  • Grandell, J. (1991). Aspects of Risk Theory. Springer, New York.
  • Huang, T., Zhao, R. and Tang, W. (2009). Risk model with fuzzy random individual claim amount. Europ. J. Operat. Res. 192, 879–890.
  • Hult, H. and Lindskog, F. (2011). Ruin probabilities under general investments and heavy-tailed claims. Finance Stoch. 15, 243–265.
  • Paulsen, J. (1998). Sharp conditions for certain ruin in a risk process with stochastic return on investment. Stoch. Process. Appl. 75, 135–148.
  • Piscitello, C. (2012). Optimal reinsurance and investment in an insurance risk model. Master's Thesis, University of Padova (in Italian).
  • Schäl, M. (2004). On discrete-time dynamic programming in insurance: exponential utility and minimizing the ruin probability. Scand. Actuarial J. 3, 189–210.
  • Schäl, M. (2005). Control of ruin probabilities by discrete-time investments. Math. Meth. Operat. Res. 62, 141–158.
  • Schmidli, H. (2002). On minimizing the ruin probability by investment and reinsurance. Ann. Appl. Prob. 12, 890–907.
  • Schmidli, H. (2008). Stochastic Control in Insurance. Springer, London.
  • Wang, R., Yang, H. and Wang, H. (2004). On the distribution of surplus inmediately after ruin under interest force and subexponential claims. Insurance Math. Econom. 35, 703–714.
  • Willmot, G. E. and Lin, X. S. (2001). Lundberg Approximations for Compound Distributions with Insurance Applications (Lecture Notes Statist. 156). Springer, New York.
  • Xiong, S. and Yang, W. S. (2011). Ruin probability in the Cramér-Lundberg model with risky investments. Stoch. Process. Appl. 121, 1125–1137. \endharvreferences