Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Stationary distribution of the surplus process in a risk model with a continuous type investment

  • Received : 2016.07.28
  • Accepted : 2016.09.06
  • Published : 2016.09.30
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Abstract

In this paper, we stochastically analyze the continuous time surplus process in a risk model which involves a continuous type investment. It is assumed that the investment of the surplus to other business is continuously made at a constant rate, while the surplus process stays over a given sufficient level. We obtain the stationary distribution of the surplus level and/or its moment generating function by forming martingales from the surplus process and applying the optional sampling theorem to the martingales and/or by establishing and solving an integro-differential equation for the distribution function of the surplus level.

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References

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