Optimality of Two-Parameter Strategies in Stochastic Control

Yamazaki, Kazutoshi

doi:10.1007/978-3-319-77643-9_2

Cited by 1 publication

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References 54 publications

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“…For example, Avram et al [2] proved optimality for general spectrally negative Lévy processes. Furthermore, in expanded situations that deal with two-sided singular control problems, Baurdoux-Yamazaki [3] and Yamazaki [17] proved optimality for general spectrally negative Lévy processes. As with the spectrally negative case, some previous studies have considered spectrally positive Lévy processes.…”

Section: Introductionmentioning

confidence: 99%

On the optimality of double barrier strategies for Lévy processes

Noba¹

2019

Preprint

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This paper studies de Finetti's optimal dividend problem with capital injection. We confirm the optimality of a double barrier strategy when the underlying risk model follows a Lévy process that may have positive and negative jumps. The main result in this paper is a generalization of [2, Theorem 3], which is the spectrally negative case, and [4, Theorem 3.1], which is the spectrally positive case. In contrast with the spectrally one-sided cases, double barrier strategies cannot be handled by using scale functions to obtain some properties of the expected net present values (NPVs) of dividends and capital injections. Instead, to obtain these properties, we observe changes in the sample path (and the associated NPV) when there is a slight change to the initial value or the barrier value.Recently, de Finetti's optimal dividend problem for Lévy processes with two-sided jumps has been studied. Some previous studies have considered de Finetti's optimal dividend problem without bail-outs. In particular, double or mixed-exponential jump diffusion processes have been discussed. For example, Bo et al.[6] computed the expected net present values (NPVs) of dividends of barrier strategies and gave numerical results for double exponential jump diffusion processes. Yin et al.[18] computed the expected NPVs of dividends of barrier strategies for mixed-exponential jump diffusion processes. and Yin et al.[19] claim to have proven the optimality of the barrier strategy for more general Lévy processes with two-sided jumps, but their proofs seem to have some flaws. In addition to these studies, Li et al.[11] gave some computational results that seem to provide the expected NPVs of dividends and capital injections of double barrier strategies for double-exponential jump diffusion processes. Overall, though, no existing paper seems to prove the optimality of any strategy.

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Section: Introductionmentioning

confidence: 99%

On the optimality of double barrier strategies for Lévy processes

Noba¹

2019

Preprint

View full text Add to dashboard Cite

show abstract

Optimality of Two-Parameter Strategies in Stochastic Control

Cited by 1 publication

References 54 publications

On the optimality of double barrier strategies for Lévy processes

On the optimality of double barrier strategies for Lévy processes

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