Asymptotic expansion for some local volatility models arising in finance

Albeverio, Sergio; Cordoni, Francesco; Persio, Luca Di; Pellegrini, Gregorio

doi:10.1007/s10203-019-00247-w

Cited by 6 publications

(3 citation statements)

References 55 publications

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“…Performing a small-noise expansion [23,31,32], we can expand Equation (24) around := 1 K , so that, using the new variables:…”

Section: Moments Estimates For a Stochastic Initial Conditionmentioning

confidence: 99%

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On the Emergence of the Deviation from a Poisson Law in Stochastic Mathematical Models for Radiation-Induced DNA Damage: A System Size Expansion

Cordoni

2023

Entropy

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In this paper, we study the system size expansion of a stochastic model for radiation-induced DNA damage kinetics and repair. In particular, we characterize both the macroscopic deterministic limit and the fluctuation around it. We further show that such fluctuations are Gaussian-distributed. In deriving such results, we provide further insights into the relationship between stochastic and deterministic mathematical models for radiation-induced DNA damage repair. Specifically, we demonstrate how the governing deterministic equations commonly employed in the field arise naturally within the stochastic framework as a macroscopic limit. Additionally, by examining the fluctuations around this macroscopic limit, we uncover deviations from a Poissonian behavior driven by interactions and clustering among DNA damages. Although such behaviors have been empirically observed, our derived results represent the first rigorous derivation that incorporates these deviations from a Poissonian distribution within a mathematical model, eliminating the need for specific ad hoc corrections.

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“…Performing a small-noise expansion [23,31,32], we can expand Equation (24) around := 1 K , so that, using the new variables:…”

Section: Moments Estimates For a Stochastic Initial Conditionmentioning

confidence: 99%

“…Performing a small-noise expansion [ 23 , 31 , 32 ], we can expand Equation ( 24 ) around

, so that, using the new variables:

we can see that the small noise expansion to the lowest order does coincide with the linear FP Equation ( 14 ).…”

Section: Theory and Calculationsmentioning

confidence: 99%

On the Emergence of the Deviation from a Poisson Law in Stochastic Mathematical Models for Radiation-Induced DNA Damage: A System Size Expansion

Cordoni

2023

Entropy

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“…The usefulness of such expansions has been pointed out very early in many contexts, including differential geometry, analysis, quantum mechanics and statistical mechanics, see, e.g. [3,4,5,6,7,8,14,15,18,19,20,21,22,23,24,30,35,41,42,43,45,46,47,49,52,59,60,61,62,63] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Borel summation of the small time expansion of some SDE’s driven by Gaussian white noise

Albeverio

Smii

2019

Asymptotic Analysis

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We consider stochastic differential equations with a drift term of gradient type and driven by Gaussian white noise on R d . Particular attention is given to the kernel p t , t ≥ 0 of the transition semigroup associated with the solution process.Under some rather strong regularity and growth assumptions on the coefficients, we adapt previous work by Thierry Hargé on Schrödinger operators and prove that the small time asymptotic expansion of p t , t > 0 is Borel summable.We also briefly indicate some extensions and applications.

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Asymptotic Expansion for a Black–Scholes Model with Small Noise Stochastic Jump-Diffusion Interest Rate

Cordoni

Persio

2021

Geometry and Invariance in Stochastic Dynamics

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Asymptotic expansion for some local volatility models arising in finance

Cited by 6 publications

References 55 publications

On the Emergence of the Deviation from a Poisson Law in Stochastic Mathematical Models for Radiation-Induced DNA Damage: A System Size Expansion

On the Emergence of the Deviation from a Poisson Law in Stochastic Mathematical Models for Radiation-Induced DNA Damage: A System Size Expansion

Borel summation of the small time expansion of some SDE’s driven by Gaussian white noise

Asymptotic Expansion for a Black–Scholes Model with Small Noise Stochastic Jump-Diffusion Interest Rate

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