Geodesic
Bounds of Ruin Probabilities for Insurance Companies in the Presence of Stochastic Volatility on Investments
Mohamed Badaoui1 ; Begoña Fernández2
1 Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Zacatenco, IPN. Gustavo A. Madero, 07738 México Mexico
2 Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM), Coyoacan 04510, México Mexico
ESAIM. Proceedings, Tome 31 (2011), pp. 40-54.

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In this work we consider a model of an insurance company where the insurer has to face a claims process which follows a Compound Poisson process with finite exponential moments. The insurer is allowed to invest in a bank account and in a risky asset described by Geometric Brownian motion with stochastic volatility that depends on an external factor modelled as a diffusion process. By using exponential martingale techniques we obtain upper and lower bounds for the ruin probabilities, that recover the known bounds for constant volatility models. Finally we apply the results to a truncated Scott model.
DOI : 10.1051/proc/2011003

Mohamed Badaoui 1 ; Begoña Fernández 2

1 Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Zacatenco, IPN. Gustavo A. Madero, 07738 México Mexico
2 Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM), Coyoacan 04510, México Mexico 
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     title = {Bounds of {Ruin} {Probabilities} for {Insurance} {Companies} in the {Presence} of {Stochastic} {Volatility} on {Investments}},
     journal = {ESAIM. Proceedings},
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Mohamed Badaoui; Begoña Fernández. Bounds of Ruin Probabilities for Insurance Companies in the Presence of Stochastic Volatility on Investments. ESAIM. Proceedings, Tome 31 (2011), pp. 40-54. doi : 10.1051/proc/2011003. http://geodesic.mathdoc.fr/articles/10.1051/proc/2011003/

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