Abstract

Optimal Dynamic Portfolio Selection and Dividend Distribution Policy for a Corporation with Controllable Risk

Michael Taksar

Department of Applied Mathematics
State University of New York at Stony Brook

We consider a problem in which the liquid assets or reserves of a company are modeled by a diffusion process. At each moment of time the management of the company makes a decision of the amount of dividends paid-out to the shareholders. There is also a possibility to reduce risk exposure by conducting a less aggressive business activity, which also results in a smaller potential profit. Mathematically this corresponds to decreasing simultaneously drift and diffusion coefficients of the controlled process. In addition the reserve of the company can be invested in a stock market in which asset prices follows Black-Scholes model.
Of a particular interest is the example of an insurance company, in which the risk control gets of a more tangible form, such as reinsurance. We look at different types of reinsurance currently employed by the insurance companies, such as proportional, proportional with liabilities, excess-of-loss and formulate the corresponding stochastic control models without and with controllable investments. The later means that at each moment the company decides what fraction of its reserve to put in risky and risk-free assets. For each of the cases the optimal policy is found and described in a close form.