SEMINAIRE LABO - Jacques PRINTEMS

Par Jacques Printems, Université de Créteil
Abstract : In this work, we introduce a differential model based on a
partial differential equation (PDE) in order to numerically evaluate the
Best Estimate of an insurance company in the case of saving contracts
with a surrender option. The main idea is to modelize the profit-sharing
policy of the company by means of a single risk factor x embedded with
the interest rate r in the revalorization formula r_s=f(t,x,r) and in
the surrender rate model mu=g(t,x,r). The numerical tool needs to be
sufficiently flexible in order to allow the modification by the insurer
of the risk factors' dynamics and the functions f and g.

We will also introduce the early surrender case on the similar model of
early exercices options. In this case, the PDE has to be replaced by a
variational inequality.

Eventually, we will see that these classes of numerical methods yield a
significant numerical cost reduction during the implementation of an
ORSA process.