Optimal dividend strategies in a dual model with capital injections. (English) Zbl 1194.91188
Summary: We study three types of practical optimization problems faced by a firm that can control its liquid reserves by paying dividends and by issuing new equity. In the first problem, we consider the classical dividend problem without equity issuance. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of issuing new equity over strategies associated with positive reserves at all times. The third problem has the same objective as the second one, but with no constraints on the reserves. Under the assumption of proportional transaction costs, we identify the value functions and the optimal strategies. We also present the relationship between the three problems.
MSC:
| 91G50 | Corporate finance (dividends, real options, etc.) |
| 91B16 | Utility theory |
| 60H05 | Stochastic integrals |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
optimal dividend; singular stochastic control; jump diffusion processes; Hamilton-Jacob-Bellman equation; capital injectionsReferences:
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