Optimal dividend and capital injection strategy with excess-of-loss reinsurance and transaction costs

Gongpin Cheng; Rongming Wang; Dingjun Yao

doi:10.3934/jimo.2017051

Article Contents

2018, Volume 14, Issue 1: 371-395. Doi: 10.3934/jimo.2017051

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Optimal dividend and capital injection strategy with excess-of-loss reinsurance and transaction costs

1.
School of Economics, Nanjing University of Finance and Economics, Nanjing 210023, China
2.
School of Statistics, East China Normal University, Shanghai 200062, China
3.
School of Finance, Nanjing University of Finance and Economics, Nanjing 210023, China

^* Corresponding author
^* Corresponding author

Received: July 2015

Revised: December 2016

Early access: June 2017

Published: January 2018

The authors are grateful to the two anonymous referees for their valuable suggestions. This work was supported by the National Natural Science Foundation of China (11571113,11231005,71471081,71671082), the Humanities and Social Sciences Project of the Ministry Education of China (15YJC910008), the Program of Shanghai Subject Chief Scientist (14XD1401600), the 111 Project (B14019), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (15KJB110009).

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Abstract

This article deals with an optimal dividend, reinsurance and capital injection control problem in the diffusion risk model. Under the objective of maximizing the insurance company's value, we aim at finding the joint optimal control strategy. We assume that there exist both the fixed and proportional costs in control processes and the excess-of-loss reinsurance is "expensive". We derive the closed-form solutions of the value function and optimal strategy by using stochastic control methods. Some economic interpretations of the obtained results are also given.

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Mathematics Subject Classification: Primary: 47N10, 97K80.

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References

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