Displaying similar documents to “Stochastic invariance and consistency of financial models”

On a stochastic SIR model

Elisabetta Tornatore, Stefania Maria Buccellato (2007)

Applicationes Mathematicae

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We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.

Stochastic differential inclusions

Michał Kisielewicz (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

Models for stochastic mortality

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.

Stochastic differential inclusions

Michał Kisielewicz (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The definition and some existence theorems for stochastic differential inclusion dZₜ ∈ F(Zₜ)dXₜ, where F and X are set valued stochastic processes, are given.