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Giorgio Ferrari

Publications and source records attributed to Giorgio Ferrari.

At least 19 recordsLinked to original sources
arXiv2026

Optimal Retirement Choice under Age-dependent Force of Mortality

This paper examines optimal investment, consumption, and retirement timing under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with a random time horizon, featuring wealth, labor income, and the force of mortality. To address this problem, we transform it into its dual form, which is a finite time horizon, three-dimensional optimal stopping problem with joint dynamics. We establish the existence of an optimal retirement boundary that separates the state space into continuation and stopping regions. We derive regularity of the optimal stopping value function, prove that the dual boundary is locally Lipschitz, and characterize the boundary as the unique solution to a nonlinear integral equation, which is solved numerically. In the original coordinates, the agent retires whenever her wealth exceeds an age- , labor-income-, and force-of-mortality-dependent transformation of the optimal stopping boundary. We also provide numerical illustrations of the optimal strategies, including sensitivity analyses of the optimal retirement boundary with respect to the relevant model parameters.

math.OC↗
arXiv2026

On the Singular Control of a Diffusion and its Running Infimum or Supremum

We study a class of singular stochastic control problems for a one-dimensional diffusion $X$ in which the performance criterion to be optimised depends explicitly on the running infimum $I$ (or supremum $S$) of the controlled process. We introduce two novel integral operators that are consistent with the Hamilton-Jacobi-Bellman equation for the resulting two-dimensional singular control problems. The first operator involves integrals where the integrator is the control process of the two-dimensional process $(X,I)$ or $(X,S)$; the second operator concerns integrals where the integrator is the running infimum or supremum process itself. Using these definitions, we prove a general verification theorem for problems involving two-dimensional state-dependent running costs, costs of controlling the process, costs of increasing the running infimum (or supremum) and exit times. Finally, we apply our results to explicitly solve an optimal dividend problem in which the manager's time-preferences depend on the company's historical worst performance.

math.OC↗
arXiv2026

On Mean-field Singular Stochastic Control Problems

We study a class of mean-field control (MFC) problems with singular controls over a finite horizon, allowing for general dependence of the cost functional on the measure argument. We derive an auxiliary mean-field game (MFG) with singular controls, which we refer to as a potential MFG, and show that, under suitable convexity assumptions, any solution to this potential MFG yields a solution to the original MFC problem. We apply this general result to a version of the classical Monotone Follower Problem by I. Karatzas and S. E. Shreve (SIAM Journal on Control and Optimization 22(6), pp. 856-877, 1984) with scalar mean-field interaction. The associated potential MFG with singular controls is solved by exploiting its connection with optimal stopping for the optimization step and by a suitable application of the Kakutani-Fan-Glicksberg fixed-point theorem. In the case of strategic complementarities, the mean-field equilibrium (and hence the optimal policy of the original MFC problem) is characterized by a continuous nonincreasing free boundary that uniquely solves a nonlinear integral equation. To the best of our knowledge, this is the first paper to provide a complete characterization of the optimal policy in a finite-horizon mean-field singular stochastic control problem.

math.OC↗
arXiv2026

Latent Fragility and Clustered Withdrawals in Dynamic Banks Runs

Using a mean-field game framework, we study a dynamic model of bank runs in which more withdrawals raise the risk of bank failure. Even though depositors receive gradual and idiosyncratic shocks, withdrawals occur in clusters. The main mechanism is latent fragility: run-prone depositors accumulate gradually over time and may prefer to wait individually, but they withdraw together once collective exit becomes self-fulfilling. We establish equilibrium existence and characterize earliest-run and latest-run equilibria. The clustering mechanism arises whether depositor heterogeneity is discrete or continuous. A common aggregate state coordinates withdrawal timing and leads to a unique threshold equilibrium.

econ.TH↗
arXiv2026

On a Merton Problem with Irreversible Healthcare Investment

We propose a tractable dynamic framework for the joint determination of optimal consumption, portfolio choice, and irreversible healthcare investment. Our model is based on Merton's portfolio and consumption problem, where, in addition, the agent can optimally choose the time at which she undertakes healthcare investment at a fixed continuous rate. Health depreciates with age and directly affects the agent's force of mortality, so that investment in healthcare reduces the agent's mortality risk. The resulting optimization problem is formulated as a stochastic control-stopping problem with a random time horizon and state variables given by the agent's wealth and health capital. We transform this problem into its dual version, which is a two-dimensional optimal stopping problem with interconnected dynamics. Regularity of the optimal stopping value function is derived, and the related free boundary is characterized through a nonlinear integral equation, which we compute numerically. In the original coordinates, the agent thus invests in healthcare whenever her wealth exceeds a health-dependent transformed version of the optimal stopping boundary. We also provide numerical illustrations of the optimal strategies and discuss some financial implications.

math.OC↗
arXiv2026

Stationary Mean-Field Games of Singular Control under Knightian Uncertainty

In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an Itô diffusion via one-sided singular stochastic control, aiming to maximize a long-term average reward criterion. The mean-field interaction is of scalar type through the stationary distribution of the population. Due to the presence of uncertainty, the problem involves the study of a stochastic zero-sum game, where the decision maker chooses the best singular control policy, while the adversarial player selects the worst probability measure. Using a constructive approach, we prove existence and uniqueness of a stationary mean-field equilibrium. Finally, we provide a stylized numerical benchmark of dirty-capacity reduction under ambiguity and analyze the impact of uncertainty on the mean-field equilibrium.

math.OC↗
arXiv2026

Continuous Differentiability of the Value Function for Infinite-Dimensional Finite-Horizon Optimal Stopping and Related Variational Inequalities

This paper studies finite-horizon optimal stopping problems for semilinear stochastic evolution equations in real, separable Hilbert spaces, together with their associated parabolic variational inequalities. We prove continuous differentiability of the value function in infinite dimensions, thereby obtaining a smooth-fit principle for the corresponding optimal stopping problem. The analysis has two parts. First, we prove existence and uniqueness, in a suitable weighted class, of a mild solution to the variational inequality and identify it with the optimal stopping value function. We also establish local spatial Lipschitz continuity of the value function by probabilistic methods, without requiring any smoothing property of the underlying transition semigroup. Second, under a global regularizing assumption on this semigroup, we prove higher-order spatial regularity: the value function is continuously Fréchet differentiable and its gradient is locally Hölder continuous. The abstract results are then applied to a stochastic heat equation with additive noise.

math.PR↗
arXiv2026

Optimal Policy Characterization for a Class of Multi-Dimensional Ergodic Singular Stochastic Control Problems

In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost of control is proportional to the magnitude of adjustments. This paper characterizes the optimal policy and the value in a class of multi-dimensional ergodic singular stochastic control problems. These problems involve a linearly controlled one-dimensional stochastic differential equation, whose coefficients, along with the cost functional to be optimized, depend on a multi-dimensional uncontrolled process Y. We first provide general verification theorems providing an optimal control in terms of a Skorokhod reflection at Y-dependent free boundaries, which emerge from the analysis of an auxiliary Dynkin game. We then fully solve two two-dimensional optimal inventory management problems. To the best of our knowledge, this is the first paper to establish a connection between multi-dimensional ergodic singular stochastic control and optimal stopping, and to exploit this connection to achieve a complete solution in a genuinely two-dimensional setting.

math.OC↗
arXiv2026

Robust Ergodic Control of Jump-Diffusion Systems under Drift and Intensity Uncertainty

We study a regulation problem for stochastic systems subject to both continuous fluctuations and rare but significant shocks, modeled as a jump-diffusion with uncertainty in both the drift and the jump intensity. Such settings arise in applications including inventory control, cash management, and capacity planning. We formulate the problem as a robust ergodic singular control problem in which a decision maker applies upward and downward interventions while accounting for model ambiguity through entropy-penalized distortions. The resulting max-min problem involves a long-run average performance criterion. We show that the associated Hamilton--Jacobi--Bellman equation reduces to a nonlinear integro-differential free-boundary problem with a tractable structure. The worst-case model exhibits a bang-bang form, and the optimal policy is characterized by reflecting barriers. Under exponentially distributed jumps, the problem further reduces to a system of ordinary differential equations, enabling efficient numerical computation.

math.OC↗
arXiv2026

Existence and uniqueness results for a mean-field game of optimal investment

We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-field equilibrium relies on a priori estimates and the study of nonlinear integral equations, but employs different techniques for the finite and infinite horizon cases. Additionally, we investigate the deterministic counterpart of the mean-field game under study.

math.OC↗
arXiv2026

High-precision automated setting of arbitrary magnitude and phase of Mach-Zehnder interferometers for scalable optical computing

Photonic technologies offer promising solutions to the power consumption, bandwidth constraints and latency limits of electronic hardware used in high-performance computing and artificial intelligence. Recently, many studies have proposed and successfully demonstrated photonic accelerators based on integrated meshes of Mach-Zehnder interferometers (MZIs), enabling matrix-vector multiplications directly in the optical domain. While being fast and energy efficient, these photonic architectures still struggle to get the required precision for such applications, because setting the complex coefficients of MZI tunable gates with a high accuracy is still an unsolved problem. This work demonstrates high-precision automated setting and stabilization of MZI-based optical gates with a resolution of 7.01 and 8.04 bits for the output power and phase, respectively. Demonstration is achieved on a multistage silicon photonic circuit comprising a coherent input vector generator, an MZI matrix-vector multiplier, and a coherent receiver for phase measurement. The proposed control strategy can configure the MZIs to any desired working point, without any prior calibration or complex algorithm for the correction of hardware non-idealities, and prevents the propagation of programming errors, thus allowing scalability towards optical processors of large size.

physics.optics↗
arXiv2026

Sequential Monitoring and Control of a Silicon Photonic Coherent Beam Adder and Analyzer

Joint communication and sensing applications require devices that can analyze multiple electromagnetic waves and process them in real time directly in the analog domain. In optics, the growing maturity of photonic integrated platforms allows the fabrication of complex circuits that can perform such operations, but their large number of sensors and actuators requires scalable control strategies to efficiently monitor and actively stabilize their functionality at runtime. In this work, we report on a multi-aperture silicon photonic programmable circuit that operates both as a coherent beam adder and a multi-aperture beam analyzer. The circuit consists of a reconfigurable mesh of Mach-Zehnder interferometers controlled through monolithically integrated electronic circuits, which are used to serialize/deserialize the readout of integrated sensors and the driving of actuators with a time-multiplexed addressing scheme. The circuit operation is validated in a communication and sensing scenario, where the photonic chip is used to simultaneously receive a 25 Gbit/s high-speed transmission and to measure the phase difference between the input light beams.

physics.optics↗
arXiv2026

Exploratory Optimal Stopping: A Singular Control Formulation

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is represented by the probability of stopping within a given time-specifically, a bounded, non-decreasing, càdlàg control process. To encourage exploration and facilitate learning, we introduce a regularized version of the problem by penalizing the performance criterion with the cumulative residual entropy of the randomized stopping time. The regularized problem takes the form of an (n+1)-dimensional degenerate singular stochastic control with finite-fuel, where the regularized free boundary becomes the graph of a function mapping the state variable of the original stopping problem into the probability of stopping. We address this singular control problem through the dynamic programming principle, which enables us to identify the unique optimal exploratory strategy. Finally, we propose both model-based and model-free reinforcement learning algorithms tailored for exploratory optimal stopping problems. We establish policy improvement guarantees for the proposed algorithms. Moreover, the model-free method is of actor-critic type and it is scalable in high-dimensions under neural network parameterization.

math.OC↗
arXiv2026

Optimal Consumption and Portfolio Choice with No-Borrowing Constraint in the Kim-Omberg Model: The Complete Market Case

In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg model, the stochastic factor represents the expected excess return of the risky asset. It is perfectly negatively correlated with shocks to the risky asset, and follows an Ornstein-Uhlenbeck process, thereby capturing the mean reversion of expected excess returns-a feature well supported by empirical evidence in financial markets. The investor seeks to maximize expected utility from consumption, subject to the constraint that wealth remains nonnegative at all times. To address the dynamic no-borrowing constraint, we use Lagrange duality to transform the primal problem into a singular control problem in the dual space. We then characterize the solution to the dual singular control problem via an auxiliary two-dimensional optimal stopping problem featuring stochastic volatility, and subsequently retrieve the primal value function as well as the optimal portfolio and consumption plans. Finally, a numerical study is conducted to derive economic and financial implications.

math.OC↗
arXiv2026

Variational inequalities and smooth-fit principle for singular stochastic control problems in Hilbert spaces

We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let $(D,\mathcal{M},μ)$ be a finite measure space and consider the Hilbert space $H:=L^2(D,\mathcal{M},μ; \mathbb{R})$. Let then $X$ be an $H$-valued stochastic process on a suitable complete probability space, whose evolution is determined through an SPDE driven by a self-adjoint linear operator $\mathcal{A}$ and affected by a cylindrical Brownian motion. The evolution of $X$ is controlled linearly via an $H$-valued control consisting of the direction and the intensity of action, a real-valued nondecreasing right-continuous stochastic process, adapted to the underlying filtration. The goal is to minimize a discounted convex cost-functional over an infinite time-horizon. By combining properties of semiconcave functions and techniques from viscosity theory, we first show that the value function of the problem $V$ is a {$C^{1,\mathrm{Lip}}(H)$}-viscosity solution to the corresponding dynamic programming equation, which here takes the form of a variational inequality with gradient constraint. Then, by allowing the decision maker to choose only the intensity of the control and requiring that the given control direction $\hat{n}$ is an eigenvector of the linear operator $\mathcal{A}$, we establish that the directional derivative $V_{\hat{n}}$ is of class $C^1(H)$, hence a second-order smooth-fit principle in the controlled direction holds for $V$. This result is obtained by exploiting a connection to optimal stopping and combining results and techniques from convex analysis and viscosity theory.

math.OC↗
arXiv2026

Reinforcement Learning in Real Option Models

We investigate an entropy-regularized reinforcement learning (RL) approach to optimal stopping problems motivated by real option models. Classical stopping rules are strict and non-randomized, limiting natural exploration in RL settings. To address this, we introduce entropy regularization, allowing randomized stopping policies that balance exploitation and exploration. We derive an explicit analytical solution to the regularized problem and prove convergence of the associated free boundary to the classical stopping threshold as the entropy vanishes. The regularized problem admits a natural formulation as a singular stochastic control problem. Building on this structure, we propose both model-based and model-free policy iteration algorithms to learn the optimal boundary. The model-free method operates without knowledge of system dynamics, using only trajectories from the stochastic environment. We establish convergence guarantees and illustrate strong numerical performance. This framework provides a principled and tractable approach for data-driven stopping problems under uncertainty.

math.OC↗
arXiv2025

Constructing a Nanopipette-based DNA Electro-Mechanical Device

Solid-state nanopore and nanopipette sensors are powerful devices for the detection, quantification and structural analysis of biopolymers such as DNA and proteins, especially in carrier-enhanced resistive-pulse sensing. However, hundreds of different molecules typically need to be sampled from solution and analysed to obtain statistically robust information. This limits the applicability of such sensors and complicates associated workflows. Here, we present a new strategy to trap DNA structures in the sensing region of a nanopipette through end functionalisation and nanoparticle capping. We develop a robust set of descriptors to characterise the insertion and presence of nanoparticle-DNA constructs in the nanopipette tip and, furthermore, show that they remain mobile and responsive to external electric fields over extended periods of time. This allows for repeated readout of the same DNA structure and could enable new applications for such sensors, for example in flow and in confined environments.

cond-mat.mes-hall↗
arXiv2025

Entropy Regularization in Mean-Field Games of Optimal Stopping

We study mean-field games of optimal stopping (OS-MFGs) and introduce an entropy-regularized framework to enable learning-based solution methods. By utilizing randomized stopping times, we reformulate the OS-MFG as a mean-field game of singular stochastic controls (SC-MFG) with entropy regularization. We establish the existence of equilibria and prove their stability as the entropy parameter vanishes. Fictitious play algorithms tailored for the regularized setting are introduced, and we show their convergence under both Lasry-Lions monotonicity and supermodular assumptions on the reward functional. Our work lays the theoretical foundation for model-free learning approaches to OS-MFGs.

math.OC↗