Asymptotic expansion of the expected discounted penalty function in a two-scalestochastic volatility risk model.
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
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.
Place, publisher, year, edition, pages
risk model, asymptotic expansion, stochastic volatility, singular and regular perturbation theory
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:mdh:diva-26100OAI: oai:DiVA.org:mdh-26100DiVA: diva2:755257
Subject / course
2014-10-01, U3-104, 13:00 (English)