OPTIMAL DIVIDEND PAYMENTS WHEN CASH RESERVES FOLLOW A JUMP‐DIFFUSION PROCESS

We consider a model in which a firm faces two types of liquidity risks: a Brownian risk and a Poisson risk. The firm chooses a dividend policy to maximize shareholder value. We characterize the optimal firm value and we show that the optimal dividend policy is a barrier strategy: the firm keeps cash inside when the cash reserves level is less than a critical threshold and pays cash in excess of this threshold. We also analyze the problem of insurance against the Poisson risk. We find that it is optimal for the firm to buy full insurance when its cash reserves are above a critical threshold and not to insure otherwise.