20 citations · 62 across the 13 of their papers we have counts for
21 papers
Strong regularization by noise for a class of kinetic SDEs driven by symmetric α-stable processes
Giacomo Lucertini, Stéphane Menozzi, Stefano Pagliarani
We establish strong well-posedness for a class of degenerate SDEs of kinetic type with autonomous diffusion driven by a symmetric -stable process under Hölder regularity conditi…
Nash equilibrium in a singular stochastic game between two renewable power producers with price impact
Stefano Pagliarani, Antonello Pesce, Tiziano Vargiolu
We study the singular stochastic game, formulated in Awerkin and Vargiolu (Decis. Econ. Finance 44(2), 2021), between two agents aiming at maximizing their profits by installing ph…
Numerical approximation of McKean-Vlasov SDEs via stochastic gradient descent
Ankush Agarwal, Andrea Amato, Goncalo dos Reis +1
We propose a novel approach to numerically approximate McKean-Vlasov stochastic differential equations (MV-SDE) using stochastic gradient descent (SGD) while avoiding the use of in…
Optimal Schauder estimates for kinetic Kolmogorov equations with time measurable coefficients
Giacomo Lucertini, Stefano Pagliarani, Andrea Pascucci
We prove global Schauder estimates for kinetic Kolmogorov equations with coefficients that are Hölder continuous in the spatial variables but only measurable in time. Compared to o…
Numerical solution of kinetic SPDEs via stochastic Magnus expansion
Kevin Kamm, Stefano Pagliarani, Andrea Pascucci
In this paper, we show how the Itô-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numericall…
Strong regularization by noise for kinetic SDEs
Giacomo Lucertini, Stefano Pagliarani, Andrea Pascucci
In this paper we prove strong well-posedness for a system of stochastic differential equations driven by a degenerate diffusion satisfying a weak-type Hörmander condition, assuming…
Optimal regularity for degenerate Kolmogorov equations with rough coefficients
Giacomo Lucertini, Stefano Pagliarani, Andrea Pascucci
We consider a class of degenerate equations satisfying a parabolic Hörmander condition, with coefficients that are measurable in time and Hölder continuous in the space variables.…
A Yosida's parametrix approach to Varadhan's estimates for a degenerate diffusion under the weak Hörmander condition
Stefano Pagliarani, Sergio Polidoro
We adapt and extend Yosida's parametrix method, originally introduced for the construction of the fundamental solution to a parabolic operator on a Riemannian manifold, to derive V…
On the stochastic Magnus expansion and its application to SPDEs
Kevin Kamm, Stefano Pagliarani, Andrea Pascucci
We derive the stochastic version of the Magnus expansion for linear systems of stochastic differential equations (SDEs). The main novelty with respect to the related literature is…
A Fourier-based Picard-iteration approach for a class of McKean-Vlasov SDEs with Lévy jumps
Ankush Agarwal, Stefano Pagliarani
We consider a class of Lévy-driven stochastic differential equations (SDEs) with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumed that the coefficient is bo…
Local densities for a class of degenerate diffusions
Alberto Lanconelli, Stefano Pagliarani, Andrea Pascucci
We study a class of R^d-valued continuous strong Markov processes that are generated, only locally, by an ultra-parabolic operator with coefficients that are regular w.r.t. the int…
Intrinsic Taylor formula for non-homogeneous Kolmogorov-type Lie groups
Stefano Pagliarani, Michele Pignotti
We prove an intrinsic Taylor-like formula for a class of Lie groups arising in the study of some sub-elliptic differential operators, namely the Kolmogorov operators. The estimate…
Intrinsic expansions for averaged diffusion processes
S. Pagliarani, A. Pascucci, M. Pignotti
We show that the rate of convergence of asymptotic expansions for solutions of SDEs is generally higher in the case of degenerate (or partial) diffusion compared to the elliptic ca…
The exact Taylor formula of the implied volatility
Stefano Pagliarani, Andrea Pascucci
In a model driven by a multi-dimensional local diffusion, we study the behavior of implied volatility σ and its derivatives with respect to log-strike k and maturity T near expiry…
Intrinsic Taylor formula for Kolmogorov-type homogeneous groups
Stefano Pagliarani, Andrea Pascucci, Michele Pignotti
We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the Hormander's condition. We prove an intrinsic Taylor formula with global and local bounds for the rem…
Asymptotics for -dimensional Lévy-type processes
Matthew Lorig, Stefano Pagliarani, Andrea Pascucci
We consider a general d-dimensional Levy-type process with killing. Combining the classical Dyson series approach with a novel polynomial expansion of the generator A(t) of the Lev…
A family of density expansions for Lévy-type processes
Matthew Lorig, Stefano Pagliarani, Andrea Pascucci
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local v…
Analytical expansions for parabolic equations
Matthew Lorig, Stefano Pagliarani, Andrea Pascucci
We consider the Cauchy problem associated with a general parabolic partial differential equation in dimensions. We find a family of closed-form asymptotic approximations for th…
A Taylor series approach to pricing and implied vol for LSV models
Matthew Lorig, Stefano Pagliarani, Andrea Pascucci
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility settin…
Explicit implied volatilities for multifactor local-stochastic volatility models
Matthew Lorig, Stefano Pagliarani, Andrea Pascucci
We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-st…
Pricing approximations and error estimates for local Lévy-type models with default
Matthew Lorig, Stefano Pagliarani, Andrea Pascucci
We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar Lévy-type stochasti…