Exact cash-account deflator for the G2++ model

摘要

In this paper, we shall propose a Monte Carlo simulation technique applied to a G2++ model: even when the number of simulated paths is small, our technique allows to find a precise simulated deflator. In particular, we shall study the transition law of the discrete random variable: ∫_([t, t+△t])x(τ)+y(τ)~(dτ) in the time span [t, t + △t] conditional on the observation at time t, and we apply it in a recursive way to build the different paths of the simulation. We shall apply the proposed technique to the insurance industry, and in particular to the issue of pricing insurance contracts with embedded options and guarantees.