The ruin problem for L\'evy-driven linear stochastic equations with applications to actuarial models with negative risk sums

arXiv1604.06370MaRDI QIDQ6272780

Serguei Pergamenchtchikov, Yuri Kabanov

Publication date: 21 April 2016

Abstract: We study the asymptotic of the ruin probability for a process which is the solution of linear SDE defined by a pair of independent L'evy processes. Our main interest is the model describing the evolution of the capital reserve of an insurance company selling annuities and investing in a risky asset. Let $$ be the root of the cumulant-generating function $H$ of the increment of the log price process $V$. We show that the ruin probability admits the exact asymptotic $$ as the initial capital $uoinfty$ assuming only that the law of $V_T$ is non-arithmetic without any further assumptions on the price process.

This page was built for publication: The ruin problem for L\'evy-driven linear stochastic equations with applications to actuarial models with negative risk sums

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6272780)