7. Hitting Times for Diffusion Processes and Stochastic Models in Insurance

  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.ch7

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) Hitting Times for Diffusion Processes and Stochastic Models in Insurance, in Applied Diffusion Processes from Engineering to Finance, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118578339.ch7

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:

  • asset liability management (ALM);
  • diffusion processes;
  • hitting times;
  • Merton's model;
  • stochastic insurance

Summary

This chapter deals with some basic models in stochastic insurance, such as risk theory, survival firm models and asset liability management (ALM), showing the strong interaction with models in physics and finance. It recalls some basic results on hitting times for diffusion processes. The financial literature has been developed both from theoretical and practical points of view. The financial literature has been developed both from theoretical and practical points of view. It consists of calculating the default probability of a firm. It takes into account the Merton's model. The chapter shows how an elementary diffusion model scan is used to modelize risk situations for insurance companies and how the preceding results on hitting times lead to the calculation of risk indicators imposed by the new rules of Solvency II for insurance companies and in a similar way by Basel II and the future Basel III for banks.