arXiv subjects

Chiara Benazzoli

Publications and source records attributed to Chiara Benazzoli.

4 recordsLinked to original sources

arXiv2020

Mean field games with controlled jump-diffusion dynamics: Existence results and an illiquid interbank market model

We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift, volatility and jump size, are controlled. Under fairly general conditions, we establish existence of a solution in a relaxed version of the mean field game and give conditions under which the optimal strategies are in fact Markovian, hence extending to a jump-diffusion setting previous results established in [30]. The proofs rely upon the notions of relaxed controls and martingale problems. Finally, to complement the abstract existence results, we study a simple illiquid inter-bank market model, where the banks can change their reserves only at the jump times of some exogenous Poisson processes with a common constant intensity, and provide some numerical results.

math.PR↗

arXiv2018

$\varepsilon$-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps

We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expected cost by affecting the drift as well as the jump part of their own private state process. We consider the corresponding limiting mean-field game and, under the assumption that the latter admits a regular Markovian solution, we prove that an approximate Nash equilibrium for the $n$-player game can be constructed for $n$ large enough, and provide the rate of convergence. This extends to a class of games with controlled jumps classical results in mean-field game literature. This paper complements our previous work, where in particular the existence of a mean-field game solution was investigated.

math.PR↗

arXiv2018

Feedback optimal controllers for the Heston model

We prove the existence of an optimal feedback controller for a stochastic optimization problem constituted by a variation of the Heston model, where a stochastic input process is added in order to minimize a given performance criterion. The stochastic feedback controller is searched by solving a nonlinear backward parabolic equation for which one proves the existence of a martingale solution.

math.OC↗

arXiv2017

Mild solutions to the dynamic programming equation for stochastic optimal control problems

We show via the nonlinear semigroup theory in $L^1(\mathbb{R})$ that the $1$-D dynamic programming equation associated with a stochastic optimal control problem with multiplicative noise has a unique mild solution $φ\in C([0,T];W^{1,\infty}(\mathbb{R}))$ with $φ_{xx}\in C([0,T];L^1(\mathbb{R}))$. The $n$-dimensional case is also investigated.

math.PR↗