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CLASSICAL AND IMPULSE STOCHASTIC CONTROL FOR THE OPTIMIZATION OF THE DIVIDEND AND RISK POLICIES OF AN INSURANCE FIRM
Author(s) -
Cadenillas Abel,
Choulli Tahir,
Taksar Michael,
Zhang Lei
Publication year - 2006
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.1467-9965.2006.00267.x
Subject(s) - stochastic control , dividend , bankruptcy , impulse control , dividend policy , bellman equation , optimization problem , economics , actuarial science , payment , mathematical optimization , time horizon , control (management) , optimal control , mathematical economics , mathematics , finance , psychology , psychotherapist , management
This paper deals with the dividend optimization problem for a financial or an insurance entity which can control its business activities, simultaneously reducing the risk and potential profits. It also controls the timing and the amount of dividends paid out to the shareholders. The objective of the corporation is to maximize the expected total discounted dividends paid out until the time of bankruptcy. Due to the presence of a fixed transaction cost, the resulting mathematical problem becomes a mixed classical‐impulse stochastic control problem. The analytical part of the solution to this problem is reduced to quasivariational inequalities for a second‐order nonlinear differential equation. We solve this problem explicitly and construct the value function together with the optimal policy. We also compute the expected time between dividend payments under the optimal policy.