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Optimal threshold strategies with capital injections in a spectrally negative Lévy risk model. (English) Zbl 1438.91176

Summary: This paper focuses on optimal threshold strategies for a spectrally negative Lévy (SNL) risk process with capital injections and proportional transaction costs. Restricted to solvency constraint, our model requires the shareholders of dividends prevent ruin by injecting capitals. Value function of the firm is assumed to be an expected discounted total [dividends less discounted capital injection]. Under such a setup, we derive certain key identities in connection with value function of the firm of a maximum dividend rate. Under restricted dividend rates and capital injection, we give analytical description of the maximum value function of the firm and the optimal threshold strategy explicitly.

MSC:

91G50 Corporate finance (dividends, real options, etc.)
91G05 Actuarial mathematics
93E20 Optimal stochastic control
60G51 Processes with independent increments; Lévy processes
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