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Asymptotic expansion of the expected discounted penalty function in a two-scalestochastic volatility risk model.
Mälardalen University, School of Education, Culture and Communication.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

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

surplus’ fluctuation.

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
Keyword [en]
risk model, asymptotic expansion, stochastic volatility, singular and regular perturbation theory
National Category
Probability Theory and Statistics
URN: urn:nbn:se:mdh:diva-26100OAI: diva2:755257
Subject / course
Mathematics/Applied Mathematics
2014-10-01, U3-104, 13:00 (English)
Available from: 2014-10-14 Created: 2014-10-14 Last updated: 2014-10-14Bibliographically approved

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