On the optimality of periodic barrier strategies for a spectrally positive Lévy process |
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Institution: | 1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, PR China;2. School of Management, University of China Academy of Sciences, Beijing 100190, PR China;3. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia |
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Abstract: | We study the optimal dividend problem in the dual model where dividend payments can only be made at the jump times of an independent Poisson process. In this context, Avanzi et al. (2014) solved the case with i.i.d. hyperexponential jumps; they showed the optimality of a (periodic) barrier strategy where dividends are paid at dividend-decision times if and only if the surplus is above some level. In this paper, we generalize the results for a general spectrally positive Lévy process with additional terminal payoff/penalty at ruin, and also solve the case with classical bail-outs so that the surplus is restricted to be nonnegative. The optimal strategies as well as the value functions are concisely written in terms of the scale function. Numerical results are also given. |
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Keywords: | Dividends Capital injection Lévy processes Scale functions Dual model |
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