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Optimal dividend and reinsurance in the presence of two reinsurers

Part of: Special processes Applications Markov processes

Published online by Cambridge University Press:  21 June 2016

Mi Chen  and
Kam Chuen Yuen
Mi Chen*
Affiliation:
Fujian Normal University
Kam Chuen Yuen*
Affiliation:
The University of Hong Kong
*
* Postal address: School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350108, China.
** Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. Email address: [email protected]
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Abstract

In this paper the optimal dividend (subject to transaction costs) and reinsurance (with two reinsurers) problem is studied in the limit diffusion setting. It is assumed that transaction costs and taxes are required when dividends occur, and that the premiums charged by two reinsurers are calculated according to the exponential premium principle with different parameters, which makes the stochastic control problem nonlinear. The objective of the insurer is to determine the optimal reinsurance and dividend policy so as to maximize the expected discounted dividends until ruin. The problem is formulated as a mixed classical-impulse stochastic control problem. Explicit expressions for the value function and the corresponding optimal strategy are obtained. Finally, a numerical example is presented to illustrate the impact of the parameters associated with the two reinsurers' premium principle on the optimal reinsurance strategy.

Keywords

Dividendreinsurancetransaction costsexponential premium principleoptimal reinsurance with two reinsurers

MSC classification

Primary: 60J65: Brownian motion 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60K99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 554 - 571
Copyright
Copyright © Applied Probability Trust 2016 

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