具有随机回报的最优融资问题

讨论了在随机收益条件下,具有混合因素(未分配利润和扩股)的最优融资问题.给出了价值函数满足的自由边界,用求解变分方程的方法证明了最优控制的存在性,并找到了最优控制策略.最优控制策略可以用两个临界值来描述:当资产小于较小的临界值时,公司扩股融资,但不分红利;当资产大于较小的临界值时,公司收益全部分红,但不扩股融资;当公司资产介于这两者之间时,不分红,也不扩股.

Problem of Optimal Financing Subject to Random Returns

We consider the problem of finding an optimal financing mixture of retained earnings and external equity for maximizing the value of a corporation in a stochastic environment. We show that the value function satisfies a free_boundary problem, prove the existence of the optimal policy by variational equation and get the optimal policy. We show that optimal policy can be characterized in terms of two threshold parameters equity. With asset level below the lower threshold, optimal policy is to finance the firm's growth by retaining all earnings and raising the required external equity. With asset level above the higher threshold, optimal policy is to pay all retained earnings as dividends and to bring in no new equity. Between the two thresholds, the optimal policy is to retain all earnings but not raise any external equity.