Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy

Bjarne Højgaard and Michael Taksar

Quantitative Finance, 2004, vol. 4, issue 3, 315-327

Abstract: This paper represents a model for risk management in a firm which exercises control of its risk as well as potential profit by choosing different business activities among those available to it. Furthermore, the firm has an option of investing its reserve in a financial market consisting of a risk-free asset (bond) and a risky asset (stock). The example we consider is that of a large corporation such as an insurance company, whose liquid assets in the absence of control and investments fluctuate as a Brownian motion with a constant positive drift and a constant diffusion coefficient. We interpret the diffusion coefficient as risk exposure, while drift is associated with potential profit. At each moment of time there is an option to reduce risk exposure, simultaneously reducing the potential profit, like using proportional reinsurance with another carrier for an insurance company. The company invests its reserve in a financial market, which is described by a classical Black-Scholes model. The management of the company also controls the dividend pay-outs to shareholders. The objective is to find a policy, consisting of investment strategy, risk control and dividend distribution scheme, which maximizes the expected total discounted dividends paid out until the time of bankruptcy. We apply the theory of controlled diffusions to solve the problem and show that there is a level u1>0 such that the optimal action is to distribute all the reserve in excess of u1 as dividends. Furthermore, there exists a constant x0, with x0Date: 2004
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DOI: 10.1088/1469-7688/4/3/007

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