BALANCING PROFIT POTENTIAL VERSUS RISK AND CORPORATE
   LIABILITIES. A MODEL FOR CORPORATE STRATEGY

                  Michael Taksar

 Department of Applied Mathematics, SUNY Stony Brook

The  proposed diffusion model deals with an optimal dividend
pay-out policy and risk control of a corporate entity e.g.,
an insurance company, subject to a constant liability payment
stream such as payments on bonds. 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. In the case of the insurance company the
latter means "reinsurance", that is redirecting some of its
premiums to another carrier. The objective is to  find the
optimal risk and dividend pay-out policy, which maximizes the
total discounted dividend pay-outs. 

To solve this problem we use methods and techniques of
consumption/investment models in Financial Mathematics, which
we "modernize" by application of singular stochastic control.
The optimal policy is to keep the company's reserve under a
certain optimal level, paying any excess as a dividend. The
optimal risk control policy depends on the current amount of
reserve. Its structure is very much dependent on the ratio of
the maximum expected profit and liability payments. When this
ratio is small the company should take the maximal risk
whatever its current financial status is. On the other hand,
if that ratio is high enough, then the risk as a function of
the current reserve increases until it reaches the maximal
level. This level is below the level when the dividends
should be paid out.