13. Monte Carlo Semi-Markov Simulation Methods

  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.ch13

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) Monte Carlo Semi-Markov Simulation Methods, in Applied Diffusion Processes from Engineering to Finance, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118578339.ch13

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:

  • homogeneous environment;
  • Semi-Markov Monte Carlo;
  • simulation model

Summary

The Monte Carlo method was developed in the 1940s by Stan Ulam and John von Neumann and since then it has become one of the most important tools in applied probability. Initially, it was mainly used for the calculation of definite integrals that could not be calculated analytically. The most important issue in simulation models is the “random number” generation. In this chapter, the authors are interested in the reconstruction of the distribution probability function and related values that the r.v. can assume for each year of a given horizon. The solution of the evolution equation of a semi-Markov process gives the probability distributions, in a discrete time environment or the density function in continuous processes. Additional topics discussed include Semi-Markov Monte Carlo with initial recurrence backward time in homogeneous case and the application of SMMC to claim reserving problem.