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Sharp Estimates of Ruin Probabilities for Insurance Models Involving Investments

In: Recent Developments In Mathematical Finance

Author

Listed:
  • Jin Ma

    (Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA)

  • Xiaodong Sun

    (Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA)

Abstract

In this note we introduce a general method for estimating ruin probabilities for insurance models that allows the insurance company to invest in a financial market. Our method is based on a new type of exponential martingale parametrized by a rate function. We show by examples that many existing Lundberg-type bounds can be reduced to finding an appropriate rate function. To study the asymptotics of the Lundberg bounds in such a general setting, we establish the relation between the ruin probability and a special type of storage process characterized by a generalized reflected SDE with discontinuous paths. Based on such a relation we use large deviation techniques to derive, in some special but non trivial cases, the limiting behavior of ruin probabilities, as well as the adjustment coefficients.

Suggested Citation

  • Jin Ma & Xiaodong Sun, 2001. "Sharp Estimates of Ruin Probabilities for Insurance Models Involving Investments," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 7, pages 72-84, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812799579_0007
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