32 citations · 104 across the 30 of their papers we have counts for
24 papers · 1 filter
A new probabilistic approach for mean field games of optimal stopping
Andrea Cosso, Laura D'Andolfi, Roxana Dumitrescu
We propose a novel probabilistic formulation for optimal stopping mean field games (OS-MFGs) with randomized strategies. We characterize mean field equilibria through a new class o…
Mean convergence rates for Gaussian-smoothed Wasserstein distances and classical Wasserstein distances
Andrea Cosso, Mattia Martini, Laura Perelli
We establish upper bounds for the expected -th power of the Gaussian-smoothed -Wasserstein distance between a probability measure and the corresponding empirical measure…
On smooth approximations in the Wasserstein space
Andrea Cosso, Mattia Martini
In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability.…
A Tikhonov theorem for McKean-Vlasov two-scale systems and a new application to mean field optimal control problems
Matteo Burzoni, Alekos Cecchin, Andrea Cosso
We provide a new version of the Tikhonov theorem for both two-scale forward systems and also two-scale forward-backward systems of stochastic differential equations, which also cov…
Path-dependent Hamilton-Jacobi-Bellman equation: Uniqueness of Crandall-Lions viscosity solutions
Andrea Cosso, Fausto Gozzi, Mauro Rosestolato +1
We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value functio…
BSDE Representation and Randomized Dynamic Programming Principle for Stochastic Control Problems of Infinite-Dimensional Jump-Diffusions
Elena Bandini, Fulvia Confortola, Andrea Cosso
We consider a general class of stochastic optimal control problems, where the state process lives in a real separable Hilbert space and is driven by a cylindrical Brownian motion a…
Ergodic Control of Infinite Dimensional SDEs with Degenerate Noise
Andrea Cosso, Giuseppina Guatteri, Gianmario Tessitore
The present paper is devoted to the study of the asymptotic behavior of the value functions of both finite and infinite horizon stochastic control problems and to the investigation…
Zero-sum stochastic differential games of generalized McKean-Vlasov type *
Huyen Pham, Andrea Cosso
We study zero-sum stochastic differential games where the state dynamics of the two players is governed by a generalized McKean-Vlasov (or mean-field) stochastic differential equat…
Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem
Elena Bandini, Andrea Cosso, Marco Fuhrman +1
We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic prog…
Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics
Erhan Bayraktar, Andrea Cosso, Huyên Pham
We analyze a stochastic optimal control problem, where the state process follows a McKean-Vlasov dynamics and the diffusion coefficient can be degenerate. We prove that its value f…
Randomization method and backward SDEs for optimal control of partially observed path-dependent stochastic systems
Elena Bandini, Andrea Cosso, Marco Fuhrman +1
We consider a unifying framework for stochastic control problem including the following features: partial observation, path-dependence (both with respect to the state and the contr…
Functional it{ô} versus banach space stochastic calculus and strict solutions of semilinear path-dependent equations
Andrea Cosso, Francesco Russo
Functional Itô calculus was introduced in order to expand a functional depending on time , past and present values of the process . Another possibi…
BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data
Andrea Cosso, Huyên Pham, Hao Xing
We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convexity and superlinear nonlinearity in its gradient term, via a t…
Strong-viscosity Solutions: Semilinear Parabolic PDEs and Path-dependent PDEs
Andrea Cosso, Francesco Russo
The aim of the present work is the introduction of a viscosity type solution, called strong-viscosity solution to distinguish it from the classical one, with the following peculiar…
Path-dependent equations and viscosity solutions in infinite dimension
Andrea Cosso, Salvatore Federico, Fausto Gozzi +2
Path-dependent PDEs (PPDEs) are natural objects to study when one deals with non Markovian models. Recently, after the introduction of the so-called pathwise (or functional or Dupi…
Ergodicity of robust switching control and nonlinear system of quasi variational inequalities
Erhan Bayraktar, Andrea Cosso, Huyên Pham
We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control pr…
Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations
Andrea Cosso, Cristina Di Girolami, Francesco Russo
The paper reminds the basic ideas of stochastic calculus via regularizations in Banach spaces and its applications to the study of strict solutions of Kolmogorov path dependent equ…
Long time asymptotics for fully nonlinear Bellman equations: a Backward SDE approach
Andrea Cosso, Marco Fuhrman, Huyen Pham
We study the large time behavior of solutions to fully nonlinear parabolic equations of Hamilton-Jacobi-Bellman type arising typically in stochastic control theory with control bot…
Robust feedback switching control: dynamic programming and viscosity solutions
Erhan Bayraktar, Andrea Cosso, Huyen Pham
We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non st…
Backward SDE Representation for Stochastic Control Problems with Non Dominated Controlled Intensity
Sébastien Choukroun, Andrea Cosso
We are interested in stochastic control problems coming from mathematical finance and, in particular, related to model uncertainty, where the uncertainty affects both volatility an…
A regularization approach to functional Itô calculus and strong-viscosity solutions to path-dependent PDEs
Andrea Cosso, Francesco Russo
First, we revisit functional Itô/path-dependent calculus started by B. Dupire, R. Cont and D.-A. Fournié, using the formulation of calculus via regularization. Relations with the c…
Reflected BSDEs with nonpositive jumps, and controller-and-stopper games
Sébastien Choukroun, Andrea Cosso, Huyen Pham
We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution is proved by a dou…
Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities
Andrea Cosso
We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial…
Viscosity Solutions of Path-Dependent PDEs and Non-Markovian Forward-Backward Stochastic Equations
Andrea Cosso
It is known that Markovian forward-backward stochastic differential equations provide nonlinear Feynman-Kac representation formulae for semilinear parabolic PDEs. We show that non-…