CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2012, 28(5) 535-550 DOI:      ISSN: 1001-4268 CN: 31-1256

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The Risk Model with Interest, Liquid Reserves and a Constant Dividend Barrier

Wei Jiaqin, Qiu Chunjuan

School of Finance and Statistics, East China
Normal University

Abstract��

In this paper, we consider the compound
Poisson surplus model with interest, liquid reserves and a constant
dividend barrier. When the surplus of an insurer is below a fixed
level, the surplus is kept as liquid reserves, which does not earn
interest. When the surplus attains the level, the surplus will
receive interest at a constant rate. When the surplus hits another
fixed higher lever, the excess of the surplus over this higher level
will be distributed to the shareholders as dividends. We derive a
system of integro-differential equations for the Gerber-Shiu
discounted penalty function and obtain the solutions to these
integro-differential equations. In the case where the claim sizes
are exponential distributed, we get the exact solutions of zero
discounted Gerber-Shiu function. We also get the
integro-differential equation for the expectation of the discounted
dividends until ruin which is the key to discuss the optimal
dividend barrier. And we give the exact solution in the special case
with exponential claim sizes.

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