Optimal threshold strategies with capital injections in a spectrally negative Lévy risk model

Manman Li; George Yin

doi:10.3934/jimo.2018055

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2019, Volume 15, Issue 2: 517-535. Doi: 10.3934/jimo.2018055

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Optimal threshold strategies with capital injections in a spectrally negative Lévy risk model

Manman Li^1, , and
George Yin^2,

1.
College of Economics and Business Administration, Chongqing University, Chongqing 400030, China
2.
Department of Mathematics, Wayne State University, MI, USA, 48202

* Corresponding author: Manman Li
* Corresponding author: Manman Li

Received: July 31, 2017

Revised: September 30, 2017

Early access: April 2018

Published: January 2019

The research of M. Li was supported in part by MOE Project of Humanities and Social Sciences on the west and the border area (No.14XJC910001) and the Fundamental Research Funds for the Central Universities (No.106112016CDJXY100002). The research of G. Yin was supported in part by the National Science Foundation under DMS-1207667.

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Abstract

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.

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Mathematics Subject Classification: Primary: 93E20; Secondary: 91B70, 60H30.

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Figure 1. The modified Lévy risk process

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