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General drawdown-based de Finetti optimization for spectrally negative Lévy risk processes

Part of: Stochastic systems and control Stochastic processes Mathematical economics

Published online by Cambridge University Press:  26 July 2018

Wenyuan Wang  and
Xiaowen Zhou
Wenyuan Wang*
Affiliation:
Xiamen University
Xiaowen Zhou*
Affiliation:
Concordia University
*
* Postal address: School of Mathematical Sciences, Xiamen University, Fujian, 361005, China. Email address: wwywang@xmu.edu.cn
** Postal address: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. W., Montreal, H3G 1M8, Canada. Email address: xzhou@mathstat.concordia.ca
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Abstract

For spectrally negative Lévy risk processes we consider a general version of de Finetti's optimal dividend problem in which the ruin time is replaced with a general drawdown time from the running maximum in its value function. We identify a condition under which a barrier dividend strategy is optimal among all admissible strategies if the underlying process does not belong to a small class of compound Poisson processes with drift, for which the take-the-money-and-run dividend strategy is optimal. It generalizes the previous results on dividend optimization from ruin time based to drawdown time based. The associated drawdown functions are discussed in detail for examples of spectrally negative Lévy processes.

Keywords

Spectrally negative Lévy processdrawdown timede Finetti's optimal dividend problemstochastic controlHJB inequality

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 93E20: Optimal stochastic control 91B30: Risk theory, insurance
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 513 - 542
Copyright
Copyright © Applied Probability Trust 2018 

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