TITLE:  Ruin estimates in a stochastic economic environment modulated by
a general Harris recurrent Markov chain  

Jeffrey Collamore, Laboratory of Actuarial Mathematics,
University of Copenhagen


ABSTRACT:  In the classical Cramer-Lundberg model, an insurance company
gains capital as a result of premiums and loses capital as a result of
claims.  We consider a modification of this model where the excess
capital is invested and the returns on these investments are
stochastic.  In recent years, such models have been studied in various
contexts, mainly under strong independence assumptions on the processes
involved.  Here we consider a generalization where the increments of the
process are governed by a Harris recurrent Markov chain.  We show that
this setting is sufficiently general to handle a wide variety of
econometric models for the investment returns, such as the popular
GARCH, stochastic volatility, and Wilkie models.  Ruin estimates in this
general context will be given.  Some possible extensions to
multidimensional problems will also be sketched. (Joint work with Harri
Nyrhinen.)