On the total operating costs up to default in a renewal risk model.

*(English)*Zbl 1231.91183Summary: We propose a new approach to study a general class of ruin-related quantities in the context of a renewal risk model. While the classical approaches in Sparre Andersen models have their own merits, the approach presented in this paper has its advantages from the following perspectives. (1) The underlying surplus process has the flexibility to reflect a broad range of scenarios for surplus growth including dividend policies and interest returns. (2) The solution method provides a general framework to unify a great variety of existing ruin-related quantities such as Gerber-Shiu functions and the expected present value of dividends paid up to ruin, and facilitates derivations of new ruin-related quantities such as the expected present value of total claim costs up to ruin, etc. In the end, many specific examples are explored to demonstrate its application in renewal risk models.

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

60K05 | Renewal theory |

##### Keywords:

ruin theory; phase-type distribution; piecewise-deterministic Markov process; total operating costs up to default
Full Text:
DOI

##### References:

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