A Diffusion Model for Optimal Dividend Distribution for a Company with Constraints on Risk Control

Tahir Choulli · Michael Taksar · Xun Yu Zhou

124 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Corporate Finance and Governance Probability and Risk Models

Abstract

This paper investigates a model of a corporation which faces constant liability payments and which can choose a production/business policy from an available set of control policies with different expected profits and risks. The objective is to find a business policy and a dividend distribution scheme so as to maximize the expected present value of the total dividend distributions. The main feature of this paper is that there are constraints on business activities such as inability to completely eliminate risk (even at the expense of reducing the potential profit to zero) or when such a risk cannot exceed a certain level. The case in which there is no restriction on the dividend pay-out rates is dealt with. This gives rise to a mixed regular-singular stochastic control problem. First the value function is analyzed in great detail and in particular is shown to be a viscosity solution of the corresponding Hamilton--Jacobi--Bellman (HJB) equation. Based on this it is further proved that the value function must be twice continuously differentiable. Then a delicate analysis is carried out on the HJB equation, leading to an explicit expression of the value function as well as the optimal policies.

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References

1999Continuous Martingales and Brownian Motion 1994Controlled markov processes and viscosity solutions 1984Stochastic differential equations with reflecting boundary conditions 1997Controlled diffusion models for optimal dividend pay-out 2000Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation 1999Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example 2000Optimal risk and dividend distribution control models for an insurance company

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2006CLASSICAL AND IMPULSE STOCHASTIC CONTROL FOR THE OPTIMIZATION OF THE DIVIDEND AND RISK POLICIES OF AN INSURANCE FIRM 2008Dynamic mean-variance problem with constrained risk control for the insurers 2010Pension funds with a minimum guarantee: a stochastic control approach 2009Optimal investment and reinsurance of an insurer with model uncertainty 2003Optimal dividend payouts for diffusions with solvency constraints 2004Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy

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