We link a general method for modeling random phenomena using systems of stochastic differential equations (SDEs) to the class of affine SDEs. This general construction emphasizes the central role of the Duffie-Kan system [Duffie and Kan, A yield-factor model of interest rates, Math. Finance 6 (1996) 379-406] as a model for first-order approximations of a wide class of nonlinear systems perturbed by noise. We also specialize to a two-dimensional framework and propose a direct proof of the Duffie-Kan theorem which does not passes through the comparison with an auxiliary process. Our proof produces a scheme to obtain an explicit representation of the solution once the one-dimensional square root process is assigned.

A general model system related to affine stochastic differential equations

Bernardi E.;Chuni V.;Lanconelli A.
2021

Abstract

We link a general method for modeling random phenomena using systems of stochastic differential equations (SDEs) to the class of affine SDEs. This general construction emphasizes the central role of the Duffie-Kan system [Duffie and Kan, A yield-factor model of interest rates, Math. Finance 6 (1996) 379-406] as a model for first-order approximations of a wide class of nonlinear systems perturbed by noise. We also specialize to a two-dimensional framework and propose a direct proof of the Duffie-Kan theorem which does not passes through the comparison with an auxiliary process. Our proof produces a scheme to obtain an explicit representation of the solution once the one-dimensional square root process is assigned.
Bernardi E.; Chuni V.; Lanconelli A.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/787284
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