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Approximation of Optimal Reinsurance and Dividend Payout Policies
Author(s) -
Bäuerle Nicole
Publication year - 2004
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.0960-1627.2004.00183.x
Subject(s) - reinsurance , piecewise , dividend , stochastic control , bankruptcy , upper and lower bounds , markov decision process , mathematical optimization , markov process , economics , limit (mathematics) , time horizon , dividend policy , bellman equation , dividend payout ratio , diffusion process , jump diffusion , mathematical economics , mathematics , optimal control , actuarial science , finance , jump , mathematical analysis , statistics , physics , economy , quantum mechanics , service (business)
We consider the stochastic process of the liquid assets of an insurance company assuming that the management can control this process in two ways: first, the risk exposure can be reduced by affecting reinsurance, but this decreases the premium income; and second, a dividend has to be paid out to the shareholders. The aim is to maximize the expected discounted dividend payout until the time of bankruptcy. The classical approach is to model the liquid assets or risk reserve process of the company as a piecewise deterministic Markov process. However, within this setting the control problem is very hard. Recently several papers have modeled this problem as a controlled diffusion, presuming that the policy obtained is in some sense good for the piecewise deterministic problem as well. We will clarify this statement in our paper. More precisely, we will first show that the value function of the controlled diffusion provides an asymptotic upper bound for the value functions of the piecewise deterministic problems under diffusion scaling. Finally it will be shown that the upper bound is achieved in the limit under the optimal feedback control of the diffusion problem. This property is called asymptotic optimality .