Skip to main content
Article thumbnail
Location of Repository

Ruin probabilities of the Parisian type for small claims

By Angelos Dassios and Shanle Wu

Abstract

In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this to occur, the surplus process must fall below zero and stay negative for a continuous time interval of specified length. We obtain the probability of ruin in the infinite horizon for the case when the process starts from zero and the asymptotic form of the probability of ruin in the infinite horizon for the case when the process starts from the point far above zero. We see that in the small claim case an asymptotic formula similar to Cramér’s formula is true

Topics: HA Statistics
Publisher: Department of Statistics, London School of Economics and Political Science
Year: 2008
OAI identifier: oai:eprints.lse.ac.uk:32037
Provided by: LSE Research Online

Suggested articles

Citations

  1. (1977). A class of approximations of ruin probabilities, doi
  2. (1978). A remark on \A class of approximations of ruin probabilities", doi
  3. An Introduction to Mathematical Risk Theory. doi
  4. (1991). Aspects of Risk Theory.
  5. (1997). Brownian excursions and Parisian barrier options, doi
  6. (2008). Brownian excursions in a corridor and related Parisian options. Working paper L.S.E..
  7. (2008). Brownian excursions outside a corridor and twosided Parisian options. Working paper L.S.E..
  8. (1955). Collective risk theory- a survey of the theory from the point of view of the theory of stochastic processes. The Jubilee volume of Skandia.
  9. (2006). Default risk, bankruptcy procedures and the market value of life insurance liabilities. doi
  10. (2004). Non-life Insurance Mathematics. doi
  11. (1992). On the distribution of the surplus prior to ruin. doi
  12. (1930). On the mathematical theory of risk. Skandia-Festskrift,
  13. (2000). On the moments of ruin and recovery timres. doi
  14. (1998). On the time value of ruin. doi
  15. (2008). Parisian options and Parisian ruin with exponential claims. doi
  16. (2002). Pricing parisian options by Laplace inversion,
  17. (2005). The density of the time to ruin in the classical Poisson risk model. doi
  18. (1997). The joint distribution of the time of ruin, the surplus immediately before ruin, and the de¯cit at ruin. doi
  19. (1992). The probability and severtiy of ruin in ¯nite and in¯nite time.
  20. (2008). Two-sided Parisian option with single barrier. Working paper L.S.E..
  21. (1990). When does the surplus reach a given target? doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.