Remarks on the Poisson Stochastic Process, I
K. Florek, E. Marczewski, C. Ryll-Nardzewski (1953)
Studia Mathematica
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K. Florek, E. Marczewski, C. Ryll-Nardzewski (1953)
Studia Mathematica
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Minkova, Leda D. (2009)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 60K10, 62P05. The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular...
Jan Iwanik (2007)
Applicationes Mathematicae
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This paper is an attempt to present and analyse stochastic mortality models. We propose a couple of continuous-time stochastic models that are natural generalizations of the Gompertz law in the sense that they reduce to the Gompertz function when the volatility parameter is zero. We provide a statistical analysis of the available demographic data to show that the models fit historical data well. Finally, we give some practical examples for the multidimensional models.
Francisco Jiménez Gómez, Mariano J. Valderrama Bonnet (1992)
Extracta Mathematicae
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Swishchuk, Anatoliy, Xu, Li (2011)
International Journal of Stochastic Analysis
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Aldous, David J. (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Beáta Stehlíková, Daniel Ševčovič (2009)
Kybernetika
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In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll–Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of...
Łukasz Delong (2012)
Applicationes Mathematicae
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We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which...
Mohamed Kayid, Salman Izadkhah, Dalal ALmufarrej (2016)
Applications of Mathematics
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By considering a covariate random variable in the ordinary proportional mean residual life (PMRL) model, we introduce and study a general model, taking more situations into account with respect to the ordinary PMRL model. We investigate how stochastic structures of the proposed model are affected by the stochastic properties of the baseline and the mixing variables in the model. Several characterizations and preservation properties of the new model under different stochastic orders and...
Smorodina, N.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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Xavier Bardina, Carles Rovira, Samy Tindel (2002)
Applicationes Mathematicae
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We find the asymptotic behavior of P(||X-ϕ|| ≤ ε) when X is the solution of a linear stochastic differential equation driven by a Poisson process and ϕ the solution of a linear differential equation driven by a pure jump function.