Optimal control with performance dependent dividend strategies and capital injection for spectrally negative Lévy risk processes
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Speaker: Wenyuan Wang (Xiamen University )
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Time: Oct 27, 2022, 15:00-16:00
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Location: Tencent Meeting ID 384-201-976, Passcode 221027
Abstract：Assume that the surplus process without dividend and capital injection for an insurance company evolves as a spectrally negative L\'evy process with the usual exclusion of negative subordinator or deterministic drift. Given $\ell_{2}\in(0,1)$ and $\ell_{1}\in(0,\ell_{2})$, dividends are distributed at some restricted fraction $\ell(\cdot)\in[\ell_{1},\ell_{2}]$ of the company's net income only when the company is in profitable situation, that is, the surplus process is at its running maximum. Meanwhile, the beneficiary of the dividends injects capital to ensure a non-negative risk process, so that the insurer never goes bankrupt. We consider the De Finetti's dividend problem of maximizing the difference between the expected discounted dividends and the expected discounted capital injection. The optimal value function and the optimal dividend strategy are obtained. It turns out that, corresponding to two opposite scenarios, the optimal dividend distribution rate keeps to be $\ell_{2}$ or switches from $\ell_{1}$ to $\ell_{2}$ once the surplus process hits some critical level and stays in the profitable situation. Some numerical examples are also provided.
