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Optimal dividend and reinsurance in the presence of two reinsurers

Published online by Cambridge University Press:  21 June 2016

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]

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

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