A Partial differential equation approach to multivariate risk theory

Robert J. Elliott, Tak Kuen Siu, Hailiang Yang

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We develop a new approach to ruin theory for a multi-line insurance business when the risk processes for correlated insurance policies are described by a multivariate diffusion process. A relation between the probability distribution of a hitting time in a multivariate diffusion framework and the solution of a multivariate partial differential equation is obtained. Explicit solutions are then derived for some special cases.
Original languageEnglish
Title of host publicationStochastic analysis and applications to finance
EditorsTusheng Zhang, Xunyu Zhou
Place of PublicationHackensack, N.J.
PublisherWorld Scientific
Pages111-123
Number of pages13
ISBN (Print)9789814383578
DOIs
Publication statusPublished - 2012

Publication series

NameInterdisciplinary mathematical sciences
PublisherWorld Scientific
Volume13

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Cite this

Elliott, R. J., Siu, T. K., & Yang, H. (2012). A Partial differential equation approach to multivariate risk theory. In T. Zhang, & X. Zhou (Eds.), Stochastic analysis and applications to finance (pp. 111-123). (Interdisciplinary mathematical sciences; Vol. 13). Hackensack, N.J.: World Scientific. https://doi.org/10.1142/9789814383585_0007