Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Transient and Stationary Analyses of the Surplus in a Risk Model

  • Received : 2013.09.06
  • Accepted : 2013.10.30
  • Published : 2013.11.30
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Abstract

The surplus process in a risk model is stochastically analyzed. We obtain the characteristic function of the level of the surplus at a finite time, by establishing and solving an integro-differential equation for the distribution function of the surplus. The characteristic function of the stationary distribution of the surplus is also obtained by assuming that an investment of the surplus is made to other business when the surplus reaches a sufficient level. As a consequence, we obtain the first and second moments of the surplus both at a finite time and in an infinite horizon (in the long-run).

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References

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  2. Stationary analysis of the surplus process in a risk model with investments vol.25, pp.4, 2014, https://doi.org/10.7465/jkdi.2014.25.4.915
  3. Surplus Process Perturbed by Diffusion and Subject to Two Types of Claim vol.22, pp.1, 2015, https://doi.org/10.5351/CSAM.2015.22.1.095
  4. An optimal continuous type investment policy for the surplus in a risk model vol.25, pp.1, 2018, https://doi.org/10.29220/CSAM.2018.25.1.091