Optimal dividend, capital injection and reinsurance strategies with transaction costs

WANG Rong-Ming; YAO Ding-Jun; XU Lin

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Optimal dividend, capital injection and reinsurance strategies with transaction costs

WANG Rong-Ming 1, YAO Ding-Jun 2, XU Lin 3

1. School of Finance and Statistics, East ChinaNormal University, Shanghai 200241

2. School of Finance, NanjingUniversity of Finance and Economics, Nanjing 210023

3.School of Mathematics and Computer Science,Anhui Normal University, Wuhu 241003

*Correspondence author

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Funding: the 111 Project （No.B14019）, Doctoral Program Foundation of the Ministry of Education of China （No.20110076110004）

Opened online:28 October 2014

Accepted by: none

Citation: WANG Rong-Ming, YAO Ding-Jun, XU Lin.Optimal dividend, capital injection and reinsurance strategies with transaction costs[OL]. [28 October 2014] http://en.paper.edu.cn/en_releasepaper/content/4614350

This paper investigates an optimal dividend and capital injection problemwith non-cheap excess-of-loss reinsurance policy. The insurancecompany can control its surplus by paying dividends and injecting capitals, which incur proportional and fixed transaction costs. Moreover, both insurer and reinsurer rely on theexpectation premium principle to calculate their premiums but withdifferent safety loadings. The goal of insurance company is todetermine optimal dividend, capital injection and reinsurance strategiesfor maximizing the difference between the expected discounteddividends minus the expected discounted capital injections untilthe time of bankruptcy. By solving the corresponding impulse control problem, closed-form expressions for the value functionand optimal strategy are derived.

Keywords:Dividend, Capital injection, Non-cheap excess-of-loss reinsurance, Transaction costs, Optimal strategy, Value function

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