On maximizing the present value of future dividends using stochastic control. - Ongkeko, George S., Jr (Philippine Computing Journal)
We illustrate the use of the Hamilton Jacobi Bellman (HJB) equation in solving a stochastic control problem. The method involves transforming the stochastic differential equation into a simpler form, but techniques in solving ODEs still have to be used to obtain the closed form of the solution. We also present a simple model of an insurance company whose wealth is invested in risky and risk-free assets, claims are assumed to follow a Brownian motion and proportional reinsurance is used to transfer some risk to the reinsurer. The wealth is controlled by the ratio of claims retained by the company, the proportion of wealth invested in risky and risky-free assets, and in the amount of dividend paid out. The reward function is the expected present value of future dividends and we solve the stochastic control problem using the above mentioned method. We present closed form solutions for the optimal controls and optimal reward functions.