Asymptotic expansion of the expected discounted penalty function in a two-scalestochastic volatility risk model.
In this Master thesis, we use a singular and regular perturbation theory to derive
an analytic approximation formula for the expected discounted penalty function.
Our model is an extension of Cramer–Lundberg extended classical model because
we consider a more general insurance risk model in which the compound Poisson
risk process is perturbed by a Brownian motion multiplied by a stochastic volatility
driven by two factors- which have mean reversion models. Moreover, unlike
the classical model, our model allows a ruin to be caused either by claims or by
We compute explicitly the first terms of the asymptotic expansion and we show
that they satisfy either an integro-differential equation or a Poisson equation. In
addition, we derive the existence and uniqueness conditions of the risk model with
two stochastic volatilities factors.
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