Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T00:28:31.204Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Insurance and Reinsurance Policies in the Risk Process

Published online by Cambridge University Press:  17 April 2015

A.Y. Golubin
A.Y. Golubin*
Affiliation:
Russian Academy of Sciences Design Information Technologies Center, Marshala Zhukova Street, 30-A, Odintsovo, Moscow region, 143000 Russia, E-mail: io@meim.edu.ru info@ditc.ras.ru
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The paper examines a classical risk model where both insurance and reinsurance policies are chosen by the insurer in order to minimize the expected maximal loss. We show that the optimal control problem reduces to a static case. We found that the optimal reinsurance is excess of loss reinsurance and describe the set optimal insurance policies. Such a policy providing the minimal variance of the risk left with insured turns out to be a combination of stop loss and deductible policies. The results are illustrated by two numerical examples.

Keywords

Optimal controlrisk sharinginsurancereinsurance
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 2 , November 2008 , pp. 383 - 397
Copyright
Copyright © ASTIN Bulletin 2008

References

Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J. (1986) Actuarial Mathematics. The Society of Actuaries, Itaca, Illinois.Google Scholar
Gerber, H.U. (1980) Principles of Premium Calculation and Reinsurance. In: Transactions of 21st Int. Congr. of Actuaries, 1, 137–142.Google Scholar
Gollier, C. (1994) Insurance and Precautionary Capital Accumulation in a Continuous-Time Model. Journal of Risk and Insurance, 61, 78–95.CrossRefGoogle Scholar
Golubin, A.Y. (2002) Franchise Optimization in the Static Insurance Model. Journal of Mathematical Sciences, 112, 4126–4140.CrossRefGoogle Scholar
Golubin, A.Y. (2005) Pareto-optimal Contracts in an Insurance Market. ASTIN Bulletin, 35(2), 363–378.CrossRefGoogle Scholar
Golubin, A.Y. (2006) An Optimal Insurance Policy in the Individual Risk Model Seen as a Bargaining Game. Game Theory and Applications, 11, 60–71.Google Scholar
Hipp, C. and Vogt, M. (2003) Optimal Dynamical XL Reinsurance. ASTIN Bulletin, 33, 193–207.CrossRefGoogle Scholar
Kaluszka, M. (2004) Mean-Variance Optimal Reinsurance Arrangements Scand. Actuarial J., 1, 28–41.CrossRefGoogle Scholar
Lehmann, E.L. (1959) Testing Statistical Hypotheses. Wiley and Sons, New York.Google Scholar
Ohlin, J. (1969) On a class of measures of dispersion with application to optimal insurance. ASTIN Bulletin, 5, 22–26.CrossRefGoogle Scholar
Raviv, A. (1979) The Design of an Optimal Insurance Policy. The American Economic Review, 69, 84–96.Google Scholar
Schmidli, H. (2001) Optimal Proportional Reinsurance Policies in a Dynamic Setting. Scand. Actuarial J., 55–68.CrossRefGoogle Scholar
Schmidli, H. (2002) On Minimizing the Ruin Probability by Investment and Reinsurance. Annals of Applied Probability, 12, 890–907.CrossRefGoogle Scholar
Waters, H.R. (1983) Some Mathematical Aspects of Reinsurance. Insurance: Mathematics and Economics, 2, 17–26.Google Scholar