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Optimal Financing of a Corporation Subject To Random Returns
Author(s) -
Sethi Suresh P.,
Taksar Michael I.
Publication year - 2002
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.t01-2-02002
Subject(s) - dividend , economics , earnings , bellman equation , stochastic control , equity (law) , external financing , finance , asset (computer security) , financial economics , microeconomics , econometrics , optimal control , mathematics , mathematical economics , mathematical optimization , computer science , debt , computer security , political science , law
We consider the problem of finding an optimal financing mix of retained earnings and external equity for maximizing the value of a corporation in a stochastic environment. We formulate the problem as a singular stochastic control for a diffusion process. We show that the value function satisfies a free‐boundary problem. We characterize the value function and show that the optimal policy can be characterized in terms of two threshold parameters. 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 financing. 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. We obtain an explicit solution for the value function when there is no brokerage commission in floating external equity. We provide economic interpretations of the results obtained in the paper.