Workshop PRIN20223PNJ8K

Mohamed Bahlali

Title: An equilibrium model of city with atmospheric pollution dispersion: Application to the Grand Paris Low Emission Zone

Abstract: This talk is based on two joint papers, one with Quentin Petit (EDF) and one with Eva Gossiaux (PSE). We propose a spatial model of city coupling a labour market, a residential market, and air pollution resulting from commuter traffic. Agents choose where to work and live in order to maximize their utility, by consuming goods, residential surface and by valuing air quality. Pollution dispersion is described by an advection–diffusion equation. We prove existence of equilibria, and uniqueness when the number of job locations is finite. The model is then calibrated and applied to assess the general equilibrium effects of the Grand Paris Low Emission Zone.

Abdessemed Raouf Boucekkine

Title: Differential climate games with heterogenous players

Abstract: TBA

Cristina Di Girolami

Titolo: Dam Management in the Era of Climate Change

Abstract: Climate change has a dramatic impact, particularly by concentrating rainfall into a few short periods, interspersed by long dry spells. In this context, the role of dams is crucial. We consider the optimal control of a dam, where the water level must not exceed a designated safety threshold, nor fall below a minimum level to ensure functionality and sustainability for for the outgoing river. To model dry spells and intense rainfall events, commonly referred to as water bombs, we introduce a Hawkes process, a well-known example of a self-exciting process characterised by time-correlated intensity, which endogenously reproduces the concentration of events. The problem is formulated as an optimal switching problem with constraints. We establish existence results and propose numerical methods for approximating the solution. Finally, we illustrate the main achievements of this approach through numerical examples. The main and counterintuitive result of our numerical analysis is that the optimal water level inside the dam increases with the self-exciting parameter. This result shows that, when facing the dilemma of managing the opposing risks of dam overtopping and dry spells, the former ultimately dominates the latter. In conclusion, dams will increasingly lose their role as water reserves and take on a greater role in flood protection.

Fabian Fuchs

Title: Existence of Viscosity Solutions to Abstract Cauchy Problems via Nonlinear Semigroups

Abstract:

In this work, we provide conditions for nonlinear monotone semigroups on locally convex vector lattices to give rise to a generalized notion of viscosity solutions to a related nonlinear partial differential equation. The semigroup needs to satisfy a convexity estimate, so called K-convexity, w.r.t. another family of operators, defined on a potentially larger locally convex vector lattice. We then show that, under mild continuity requirements on the bounding family of operators, the semigroup yields viscosity solutions to the abstract Cauchy problem given in terms of its generator in the larger locally convex vector lattice. We apply our results to control problems under uncertainty.

Quentin Petit

Title: Growth model with externalities for energetic transition via MFG with common external variable

Abstract : We introduce a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories and integrating environmental considerations, the framework incorporates “common noise” to capture shared uncertainties among agents about the externality variable. We establish the existence and uniqueness of the mean-field game equilibrium by reformulating the equilibrium conditions as a Forward–Backward Stochastic Differential Equation via the stochastic maximum principle, first applying a contraction-mapping argument to guarantee a unique solution, then employing the concept of weak equilibria to prove existence under more general assumptions, and finally invoking a specific monotonicity regime to reaffirm uniqueness. We provide a numerical resolution for a specified model using a fixed-point approach combined with neural network approximations.

Seyedalireza Seyedi

Title: Collaborative and Competitive Approaches in a Dynamic Model of Forest Management

Abstract: This study develops a dynamic, finite-horizon forest management model linking biomass, biodiversity, and harvest under stochastic shocks to compare collaborative and competitive approaches. Collaborative management moderates harvest, sustains ecological stocks, and raises welfare—especially with flexible endpoints—while competitive behavior underperforms on all dimensions. These gains can be decentralized with state-contingent incentives and remain robust across sensitivity analyses.

Anastasios Xepapadeas

Title: Natural resource management and biodiversity preservation

Abstract: This study develops an ecosystem management model in which species growth depends jointly on a biodiversity index (measured by the Shannon entropy) and a limiting resource (e.g., nutrients, sunlight) for which species compete. Species are harvested by multiple agents and generate provisioning, regulating, and existence values. Biodiversity not only enhances species growth but also provides additional public-good benefits, including resilience, insurance, and knowledge. The analysis characterizes cooperative solutions that internalize both private and public values, as well as non-cooperative solutions that may be myopic or dynamic but neglect public-good benefits. Both open-loop and feedback (Markov perfect) equilibria are examined. The results highlight valuation discrepancies between cooperative and non-cooperative steady states and show that non-cooperative solutions, by disregarding the role of biodiversity in growth and its public-good values, tend to promote excessive harvesting. Potential regulatory mechanisms are discussed, and future research should focus on meaningful calibration and numerical implementation of the model.

Filippo de Feo

Title: Stochastic optimal control in Hilbert spaces via viscosity solutions and applications to problems in economics

Abstract: We study stochastic optimal control problems on Hilbert spaces through the dynamic programming approach. The main challenge is that the associated Hamilton–Jacobi–Bellman equation is a PDE on a Hilbert space involving unbounded operators. I will present recent results proving $C^{1,1}$-regularity of the value function and show how this regularity enables the construction of optimal feedback controls. In the second part, I will extend this framework to stochastic control problems of interacting particle systems on Hilbert spaces. I will illustrate applications to economic models governed by stochastic partial differential equations and by stochastic delay equations.

The talk is based on:

F. de Feo, A. Święch, L. Wessels, “Stochastic optimal control in Hilbert spaces: $C^{1,1}$-regularity of the value function and optimal synthesis via viscosity solutions”, Electron. J. Probab. 30 (2025), 1-39
F. de Feo, F. Gozzi, A. Święch, L. Wessels, “Stochastic Optimal Control of Interacting Particle Systems in Hilbert Spaces and Applications”, Soon on Arxiv

Sara Biagini

Title: Climate risk mitigation via carbon markets: accounting for the lifespan of GHGs

Abstract: We study the problem of optimal climate risk mitigation with short-term emission reduction targets and long-run temperature stabilization goals in the presence of firms generating greenhouse gases with different temporal persistency and warming potential. We investigate how the pervasive notion of carbon equivalence may undermine climate risk mitigation efforts when carbon markets can be used to trade short-lived gases against long-lived ones. The findings demonstrate the vulnerability of certain emission metrics and carbon accounting standards to greenwashing and support the reporting of emissions in disaggregated form and native units of measure.

Based on a joint work with E. Biffis and K. Salehzadeh Nobari.

Michele Aleandri

Title: Reinforced dynamics for interacting agents in competitive or cooperative environments

Abstract: We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we prove almost sure convergence of agents' states, with bipartite graphs leading to non-deterministic limits and non-bipartite graphs to deterministic ones. These results are extended to reducible networks with cooperative or competitive substructures, using a hierarchical graph representation in which higher-level agents perceive lower-level agents as forcing inputs. A general framework for interacting agents under external forcing is also provided, offering a rigorous characterization of long-term behavior and synchronization phenomena in such systems.

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