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Symmetry 2018, 10(7), 276; https://doi.org/10.3390/sym10070276

Optimal Dividend and Capital Injection Problem with Transaction Cost and Salvage Value: The Case of Excess-of-Loss Reinsurance Based on the Symmetry of Risk Information

1
School of Economics and Management, North China Electric Power University, Beijing 102206, China
2
Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Beijing 102206, China
3
Lithuanian Institute of Agrarian Economics, V. Kudirkos Str. 18, LT-03105 Vilnius, Lithuania
*
Authors to whom correspondence should be addressed.
Received: 8 June 2018 / Revised: 7 July 2018 / Accepted: 9 July 2018 / Published: 12 July 2018
(This article belongs to the Special Issue Solution Models based on Symmetric and Asymmetric Information)
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Abstract

This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the fixed transaction cost incurred by capital injection and the salvage value of a company at the ruin time in order to make the surplus process more realistic. The main goal is to maximize the expected sum of the discounted salvage value and the discounted cumulative dividends except for the discounted cost of capital injection until the ruin time. By considering whether there is capital injection in the surplus process, we construct two instances of suboptimal models and then solve for the corresponding solution in each model. Lastly, we consider the optimal control strategy for the general model without any restriction on the capital injection or the surplus process. View Full-Text
Keywords: optimal dividend; capital injection; salvage value; transaction cost; excess-of-loss reinsurance optimal dividend; capital injection; salvage value; transaction cost; excess-of-loss reinsurance
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Yan, Q.; Yang, L.; Baležentis, T.; Streimikiene, D.; Qin, C. Optimal Dividend and Capital Injection Problem with Transaction Cost and Salvage Value: The Case of Excess-of-Loss Reinsurance Based on the Symmetry of Risk Information. Symmetry 2018, 10, 276.

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