Moments of claims in a Markovian environment

Bara Kim; Hwa Sung Kim

doi:10.1016/j.insmatheco.2006.07.004

Moments of claims in a Markovian environment

Bara Kim, Hwa Sung Kim

Department of Mathematics

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

22 Citations (Scopus)

Abstract

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.

Original language	English
Pages (from-to)	485-497
Number of pages	13
Journal	Insurance: Mathematics and Economics
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/j.insmatheco.2006.07.004
Publication status	Published - 2007 May

Bibliographical note

Funding Information:
We are very grateful to the referee and the editor, Rob Kaas, for valuable comments on this paper. This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).

Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.

Keywords

Circumstance process
Discounted aggregate claims
Laplace-Stieltjes transform
Moments

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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10.1016/j.insmatheco.2006.07.004

Cite this

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abstract = "This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.",

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AU - Kim, Bara

AU - Kim, Hwa Sung

N1 - Funding Information: We are very grateful to the referee and the editor, Rob Kaas, for valuable comments on this paper. This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). Copyright: Copyright 2007 Elsevier B.V., All rights reserved.

PY - 2007/5

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N2 - This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.

AB - This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.

KW - Circumstance process

KW - Discounted aggregate claims

KW - Laplace-Stieltjes transform

KW - Moments

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SN - 0167-6687

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EP - 497

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

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ER -

Moments of claims in a Markovian environment

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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