The maximum surplus before ruin in a jump-diffusion insurance risk process with dependence

Wuyuan Jiang

doi:10.3934/dcdsb.2018298

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2019, Volume 24, Issue 7: 3037-3050. Doi: 10.3934/dcdsb.2018298

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The maximum surplus before ruin in a jump-diffusion insurance risk process with dependence

Wuyuan Jiang^,

Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China

* Corresponding author: Wuyuan Jiang
* Corresponding author: Wuyuan Jiang

Received: January 31, 2018

Revised: May 31, 2018

Early access: October 2018

Published: May 2019

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Abstract

We consider a compound Poisson risk process perturbed by a Brownian motion through using a potential measure where the claim sizes depend on inter-claim times via the Farlie-Gumbel-Morgenstern copula. We derive an integro-differential equation with certain boundary conditions for the distribution of the maximum surplus before ruin. This distribution can be calculated through the probability that the surplus process attains a given level from the initial surplus without first falling below zero. The explicit expressions for this distribution are derived when the claim amounts are exponentially distributed.

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Mathematics Subject Classification: Primary: 62P05; Secondary: 91B30.

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Figure 1. $\mathcal{G}(u, 10)$ for different dependent parameters when $0\leq u< 10$

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