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.. - In: STOCHASTICS AND DYNAMICS. - ISSN 0219-4937. - ELETTRONICO. - 21:1(2021), pp. 2150001.1-2150001.17. [10.1142/S0219493721500015]
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.File | Dimensione | Formato | |
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Open Access dal 01/02/2022
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