On the ruin problem in a Markov-modulated risk model

Xin Zhang

doi:10.1007/s11009-007-9044-4

On the ruin problem in a Markov-modulated risk model

Xin Zhang

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this paper, we consider the compound Poisson risk model influenced by an external Markovian environment process, i.e. Markov-modulated compound Poisson model. The explicit Laplace transforms of Gerber–Shiu functions are obtained, while the explicit Gerber–Shiu functions are derived for the K n -family claim size distributions in the two-states case.

Original language	English
Pages (from-to)	225-238
Number of pages	14
Journal	Methodology and Computing in Applied Probability
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/s11009-007-9044-4
Publication status	Published - 2008
Externally published	Yes

Keywords

Markov additive process
Laplace transform
Gerber–Shiu function
Markov-modulated compound Poisson model

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10.1007/s11009-007-9044-4

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title = "On the ruin problem in a Markov-modulated risk model",

abstract = "In this paper, we consider the compound Poisson risk model influenced by an external Markovian environment process, i.e. Markov-modulated compound Poisson model. The explicit Laplace transforms of Gerber–Shiu functions are obtained, while the explicit Gerber–Shiu functions are derived for the K n -family claim size distributions in the two-states case.",

keywords = "Markov additive process, Laplace transform, Gerber–Shiu function, Markov-modulated compound Poisson model",

author = "Xin Zhang",

year = "2008",

doi = "10.1007/s11009-007-9044-4",

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AB - In this paper, we consider the compound Poisson risk model influenced by an external Markovian environment process, i.e. Markov-modulated compound Poisson model. The explicit Laplace transforms of Gerber–Shiu functions are obtained, while the explicit Gerber–Shiu functions are derived for the K n -family claim size distributions in the two-states case.

KW - Markov additive process

KW - Laplace transform

KW - Gerber–Shiu function

KW - Markov-modulated compound Poisson model

U2 - 10.1007/s11009-007-9044-4

DO - 10.1007/s11009-007-9044-4

M3 - Article

SN - 1387-5841

VL - 10

SP - 225

EP - 238

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 2

ER -

On the ruin problem in a Markov-modulated risk model

Abstract

Keywords

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