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Finance

2013/1 (Vol. 34)


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Abstract

English

The fall of AIG proved that the insurance business is not immune to bankruptcy, contrary to the actuarial literature which postulates that insurance firms can survive forever. In this article we model the surplus process of an insurance firm firstly by a stable Lévy process, secondly by a double exponential compound Poisson process. We compute finite-time survival and bankruptcy probabilities under such hypotheses. To achieve this, we make use of the Wiener-Hopf factorization and compute bankruptcy formulas written in terms of inverse Laplace transforms. The Abate and Whitt, and Gaver-Stehfest algorithms are used to obtain numerical estimations. This article can be viewed as an illustration of a general approach to the bankruptcy of financial institutions.

Outline

  1. Introduction
  2. Stable and Double Exponential Jump Processes
    1. Stable Lévy Processes
    2. Double Exponential Lévy Processes
  3. Bankruptcy and Survival Probabilities
    1. Derivation of a General Formula
    2. Bankruptcy and Stable Processes
      1. Finite-time bankruptcy probabilities
      2. Infinite-time bankruptcy probabilities
    3. Bankruptcy and Double Exponential Lévy Processes
      1. Finite-time bankruptcy probabilities
      2. Infinite-time bankruptcy probabilities
    4. Numerical Implementation
      1. Obtaining the values of and
      2. Double Inverse Laplace Transform
      3. Single Inverse Laplace Transform
  4. Survival Probabilities with Stable Lévy Processes
    1. Impact of the Asymmetry Parameter ?
    2. Impact of the Tail Thickness Parameter ?
    3. Impact of the Dispersion Parameter ?
    4. Impact of the Initial Surplus Level Parameter u
  5. Empirical Illustration
  6. Conclusion

To cite this article

Olivier Le Courtois, Rivo Randrianarivony, “ On the Bankruptcy Risk of Insurance Companies ”, Finance 1/2013 (Vol. 34) , p. 43-72
URL : www.cairn.info/revue-finance-2013-1-page-43.htm.

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