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| On a Dual Risk Model Perturbed by Diffusion with Dividend Threshold |
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Citation： |
Hui ZHI,Jiangyan PU.On a Dual Risk Model Perturbed by Diffusion with Dividend Threshold[J].Chinese Annals of Mathematics B,2016,37(5):777~792 |
| Page view： 1329
Net amount： 1096 |
Authors： |
Hui ZHI; Jiangyan PU |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11426151). |
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| Abstract： |
In the dual risk model, the surplus process of a company is a L\'evy
process with sample paths that are skip-free downwards. In this
paper, the authors assume that the surplus process is the sum of a
compound Poisson process and an independent Wiener process. The dual
of the jump-diffusion risk model under a threshold dividend strategy
is discussed. The authors derive a set of two integro-differential
equations satisfied by the expected total discounted dividend until
ruin. The cases where profits follow an exponential or mixtures of
exponential distributions are solved. Applying the key method of the
Laplace transform, the authors show how the integro-differential
equations are solved. The authors also discuss the conditions for
optimality and show how an optimal dividend threshold can be
calculated as well. |
Keywords： |
Dual risk model, Threshold strategy, Stochastic optimal control, Smooth pasting condition |
Classification： |
60J70, 60J75, 91B70 |
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