On finite-time ruin probabilities in a generalized dual risk model with dependence. (English) Zbl 1341.91090
Summary: In this paper, we study the finite-time ruin probability in a reasonably generalized dual risk model, where we assume any non-negative non-decreasing cumulative operational cost function and arbitrary capital gains arrival process. Establishing an enlightening link between this dual risk model and its corresponding insurance risk model, explicit expressions for the finite-time survival probability in the dual risk model are obtained under various general assumptions for the distribution of the capital gains. In order to make the model more realistic and general, different dependence structures among capital gains and inter-arrival times and between both are also introduced and corresponding ruin probability expressions are also given. The concept of alarm time, as introduced in [S. Das and M. Kratz, Insur. Math. Econ. 51, No. 1, 53–65 (2012; Zbl 1284.91223)], is applied to the dual risk model within the context of risk capital allocation. Extensive numerical illustrations are provided.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 60K10 | Applications of renewal theory (reliability, demand theory, etc.) |
Keywords:
dual (dependent) risk model; finite-time ruin probability; capital allocation; alarm time; (exponential) classical Appell polynomialsCitations:
Zbl 1284.91223References:
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