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.
|Title of host publication||Stochastic analysis and applications to finance|
|Editors||Tusheng Zhang, Xunyu Zhou|
|Place of Publication||Hackensack, N.J.|
|Number of pages||13|
|Publication status||Published - 2012|
|Name||Interdisciplinary mathematical sciences|
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