Ruin Probability in Compound Poisson Process with Investment

We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the cl...

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Main Authors: Yong Wu, Xiang Hu
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/286792
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author Yong Wu
Xiang Hu
author_facet Yong Wu
Xiang Hu
author_sort Yong Wu
collection DOAJ
description We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained.
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spelling doaj-art-d6896bd4fde547fa92f2353a22052aff2025-08-20T02:19:33ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/286792286792Ruin Probability in Compound Poisson Process with InvestmentYong Wu0Xiang Hu1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaSchool of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaWe consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained.http://dx.doi.org/10.1155/2012/286792
spellingShingle Yong Wu
Xiang Hu
Ruin Probability in Compound Poisson Process with Investment
Journal of Applied Mathematics
title Ruin Probability in Compound Poisson Process with Investment
title_full Ruin Probability in Compound Poisson Process with Investment
title_fullStr Ruin Probability in Compound Poisson Process with Investment
title_full_unstemmed Ruin Probability in Compound Poisson Process with Investment
title_short Ruin Probability in Compound Poisson Process with Investment
title_sort ruin probability in compound poisson process with investment
url http://dx.doi.org/10.1155/2012/286792
work_keys_str_mv AT yongwu ruinprobabilityincompoundpoissonprocesswithinvestment
AT xianghu ruinprobabilityincompoundpoissonprocesswithinvestment