11. Advanced Topics in Insurance: Copula Models and VaR Techniques

  1. Jacques Janssen,
  2. Oronzio Manca and
  3. Raimondo Manca
  1. Jacques Janssen,
  2. Oronzio Manca and
  3. Raimondo Manca

Published Online: 4 APR 2013

DOI: 10.1002/9781118578339.ch11

Applied Diffusion Processes from Engineering to Finance

Applied Diffusion Processes from Engineering to Finance

How to Cite

Janssen, J., Manca, O. and Manca, R. (2013) Advanced Topics in Insurance: Copula Models and VaR Techniques, in Applied Diffusion Processes from Engineering to Finance, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118578339.ch11

Publication History

  1. Published Online: 4 APR 2013
  2. Published Print: 4 MAR 2013

ISBN Information

Print ISBN: 9781848212497

Online ISBN: 9781118578339

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Keywords:

  • copula models;
  • dependence;
  • digital put options;
  • Fréchet bounds;
  • insurance;
  • Sklar theorem;
  • VaR theory

Summary

A copula C in two dimensions is a distribution function on R2 defined as a function of the two marginal distributions. The main aim of the copula is to introduce certain dependence between several asset values in finance or claim values in insurance. This chapter presents a discussion on Sklar theorem, Fréchet bounds, and digital put options. To select the best copula, the chapter introduces some relations for conditional probabilities. The aim of the VaR theory is to find, for a given risk, an amount of equity such that the probability of having a loss larger than this value is very small, for example 1%, and thus compatible with the attitude of the management against risk. The main step for the insurance company is to select the best copula corresponding to the dependence of their risks. Numerical methods or simulation should be used to approximate the unknown loss distribution function.