Julio Backhoff (Universität Wien)

Title: Exciting games and the specific relative entropy

Abstract: The laws of two continuous martingales will typically be singular to each other and hence have infinite relative entropy. But this does not need to happen in discrete time. This suggests defining a new object, the specific relative entropy, as a scaled limit of the relative entropy between the discretized laws of the martingales. This definition goes all the way back to Gantert’s PhD thesis, and in recent time Föllmer has rekindled the study of this object by for instance obtaining a novel transport-information inequality.

Mathias Beiglböck (Universität Wien)

Title: Brenier’s theorem for adapted transport I

Abstract: We develop Brenier theorems on iterated Wasserstein spaces. For a separable Hilbert space $H$ and $N\ge 1$, we construct a full-support probability $\Lambda$ on $\mathcal{P}_2^{N}(H)= \Pc_2(\ldots \Pc_2(\H)\ldots)$ that is transport regular: for every $Q$ with finite second moment, transporting $\Lambda$ to $Q$ with cost $\W_2^2$ admits a unique optimizer, and this optimizer is of Monge type. The analysis rests on a characterization of optimal couplings on $\mathcal{P}_2(H)$ and, more generally, on $\mathcal{P}_2^{\,N}(H)$ via convex potentials on the Lions lift; in the latter case we employ a new adapted version of the lift tailored to the $N$-step structure. A key idea is a new identification between optimal-transport $c$-conjugation (with $c$ given by maximal covariance) and classical convex conjugation on the lift.

A primary motivation comes from the adapted Wasserstein distance $\AW_2$: our results yield a first Brenier theorem for $\AW_2$ and characterize $\AW_2^2$-optimal couplings through convex functionals on the space of $L_2$-processes.

This is joint work with Gudmund Pammer and Stefan Schrott.

Filippo Beretta (ETH Zürich)

Title: Closed-loop strategies in partial-information leader-follower games

Abstract: In this talk I will first discuss recent results on explicit formulae (or bounds) for the specific relative entropy in terms of the quadratic variation processes of the martingales involved. Next I will describe an application of this object to prediction markets. Concretely, D. Aldous asked in an open question to determine the ‘most exciting game’, i.e. the prediction market with the highest entropy. We formalize this question as a problem of specific relative entropy optimization and characterize its optimizer even in the multiple outcomes / players setting. As a crucial step, we make an unexpected connection to the field of Monge-Ampère equations.

Luis Briceño (Universidad Técnica Federico Santa María)

Title: A dual proximal-gradient approach for variational mean field games

Abstract: In this talk, we provide a new algorithm to approximate equilibria of variational mean field game systems (MFG) with local couplings. Under suitable conditions on the coupling function, the dual of the variational formulation of the MFG reduces to the minimization of the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally Lipschitz- type condition. In this context, we provide a generalization of the proximal-gradient splitting algorithm for tackling the dual problem. We prove the convergence of our method and derive a linear convergence rate when the differentiable function is locally strongly convex. We recover classical results in the case when the gradient of the differentiable function is globally Lipschitz continuous and an already known linear convergence rate when the function is globally strongly convex. Compared with some benchmark algorithms to solve these problems, our numerical tests show similar performances in terms of the number of iterations but an important gain in the required computational time.

Anna de Crescenzo (Université Paris Cité)

Title: Mean-field control of heterogeneous systems

Abstract: We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal probability laws. We prove the well-posedness of such systems and define the control problem together with its related value function. Leveraging tools tailored for this framework, such as derivatives along flows of measures and associated Itô calculus, we establish that the value function for this control problem satisfies a Bellman dynamic programming equation in a L^2-set of Wasserstein space-valued functions. To illustrate the applicability of our approach, we present a linear-quadratic graphon model with analytical solutions, and apply it to a systemic risk example involving heterogeneous banks.

Cristopher Hermosilla (Universidad Técnica Federico Santa María)

Title: A Minimality Property of the Value Function in Optimal Control on Spaces of Probability Measures

Abstract: In this talk we study an optimal control problem with (possibly) unbounded terminal cost in the space of Borel probability measures with finite second moment. We consider a suitable weak topology rendering this space locally compact. In this setting, we show that the value function of a control problem is the minimal viscosity supersolution of an appropriate Hamilton–Jacobi–Bellman equation. Additionally, if the terminal cost is bounded and continuous, we show that the value function is the unique viscosity solution of the HJB equation.

Camilo Hernández (University of Southern California)

Title: Dynamic Schrödinger bridges beyond entropy

Abstract: Over the past decade, the Schrödinger bridge problem has emerged as a central tool for modeling the evolution of uncertainty in dynamical systems. It describes the most likely stochastic evolution connecting two observed distributions and forms the dynamic, entropy-regularized analogue of optimal transport. Unlike its static counterpart, the dynamic formulation explicitly models the temporal evolution of probability flows, a feature that has proven essential in modern generative modeling via diffusion processes, where data distributions are learned through time-dependent stochastic transformations. While the classical Schrödinger problem relies on relative entropy, which ensures analytical convenience, this choice can be restrictive: it produces diffuse stochastic trajectories and imposes a specific log-penalty structure that may not capture robustness or structural features of the system. General divergence-based penalties offer greater flexibility, allowing the model to capture alternative notions of discrepancy and sensitivity. Indeed, insights from quadratically regularized optimal transport, a static analogue of the problem considered in this project, suggest that L^2-type penalizations can induce sparsity in the transport plan, emphasizing the most relevant trajectories while downweighting minor fluctuations. In this work, we leverage stochastic control tools and convex duality to extend these ideas to the dynamic, path-space setting.

Nicolás Hernández-Santibáñez (Universidad Técnica Federico Santa María)

Title: On contract theory with multiple players and numerical algorithms

Abstract: In this talk, we investigate on static Principal–Agent problems with multiple agents and multiple principals separately. We define our problems of interest, provide some theoretical characterizations of equilibria and, based on the work of Renner and Schmedders (2015), we provide algorithms to find them in the case of rational functions. Talk based on joint works with Luis Briceño, María José Núñez and Vicente Moreno from Universidad Técnica Federico Santa María.

Emma Hubert (Université Paris Dauphine)

Title: Revisiting contract theory with volatility control

Abstract: In this talk, we revisit the resolution of continuous-time principal–agent problems with drift and volatility control, originally addressed by Cvitanić, Possamaï, and Touzi (2018) [1] through dynamic programming and second-order backward stochastic differential equations (2BSDEs), and develop new results in this framework.
We begin by introducing an alternative problem in which the principal is allowed to directly control the quadratic variation of the output process. On the one hand, the resolution of this contractible-volatility problem follows the classical methodology of Sannikov (2008) [2], thus relying on standard (first-order) BSDEs only. On the other hand, we demonstrate that the original contract form introduced in [1] allows the principal to achieve her contractible-volatility value, thereby ensuring both the optimality of this contract form and the equivalence between the original and the alternative problems. At the same time, this alternative approach reveals that the optimality of the original contract form implicitly relies on an additional duality assumption, which was not identified in [1]. This observation motivates the construction of new families of contracts—forcing and duality-corrected contracts—that remain optimal even when the duality assumption fails.
Altogether, this line of work both simplifies and strengthens the existing theory of continuous-time principal–agent problems with volatility control, and opens new directions for further extensions and applications in economics and finance.
Talk based on joint works with Alessandro Chiusolo, Dylan Possamaï, and Nizar Touzi.

Nabil Kazi-Tani (Université de Lorraine)

Title: Multi-dimensional risk-averse stochastic optimization

Abstract: We will present a stochastic optimization problem in a risk-averse setting, involving a multi-dimensional risk measure applied to a random vector with an unknown joint distribution, for which i.i.d. observations are available. We establish consistency results for this class of problems, both for the convergence of the optimal value and for the convergence of minimizers. We illustrate these results with examples involving the spectrum of matrices whose distribution is unknown.This is joint work with Simon Bartolacci (Université de Lorraine, Metz) and Pedro Pérez-Aros (Universidad de Chile, Santiago).

Anastasis Kratsios (McMaster University)

Title: The Neural Black0-Scholes Formula

Abstract: Despite its central role in option markets, the implied volatility surface (IVS) remains exceptionally difficult to calibrate to quoted call prices without breaching fundamental economic constraints. We resolve this long-standing open problem by deriving a simple, model-free, smooth $(C^{\infty})$ call-option pricing formula that provides explicit closed-form weights and biases for a trained two-layer neural network whose activation function is the Black–Scholes call-price formula.
This network approximately reconstructs the ground-truth quoted market prices within the bid–ask spread uniformly to accuracy $\mathcal{O}(1/n^2+\varepsilon)$ using $n$ neurons, guarantees no arbitrage, and has second derivative of order $\Theta(1/\varepsilon)$. For comparison, the only other neural-network paradigm with fully closed-form weights and biases achieves a slower $\mathcal{O}(1/\sqrt{n})$ convergence rate.

Daniel Kršek (ETH Zürich)

Title: Absolute Continuity in the Adapted Wasserstein Space

Abstract: We present recent results concerning the adapted Wasserstein space. We characterize absolutely continuous curves of stochastic processes by means of a probabilistic representation and use this characterization to describe geodesics in the adapted Wasserstein space. This, in turn, allows us to reformulate the transport problem as an energy minimization problem, leading to an adapted version of the Benamou–Brenier theorem. The talk is based on joint work with B. Acciaio, G. Pammer, M. Rodrigues, and S. Schrott.

Thibaut Mastrolia (University of California Berkeley)

Title: Agency Problems and Adversarial Bilevel Optimization under Uncertainty and Cyber Threats

Abstract: We study an agency problem between a holding company and its subsidiary, exposed to cyber threats that affect the overall value of the subsidiary. The holding company seeks to design an optimal incentive scheme to mitigate these losses. In response, the subsidiary selects an optimal cybersecurity investment strategy, modeled through a stochastic epidemiological SIR (Susceptible-Infected-Recovered) framework. The cyber threat landscape is captured through an L-hop risk framework with two primary sources of risk: (i) internal risk propagation via the contagion parameters in the SIR model, and (ii) external cyberattacks from a malicious external hacker. The uncertainty and adversarial nature of the hacking lead to consider a robust stochastic control approach that allows for increased volatility and ambiguity induced by cyber incidents. The agency problem is formulated as a max-min bilevel stochastic control problem with accidents. First, we derive the incentive compatibility condition by reducing the subsidiary’s optimal response to the solution of a second-order backward stochastic differential equation with jumps. Next, we demonstrate that the principal’s problem can be equivalently reformulated as an integro-partial Hamilton–Jacobi–Bellman–Isaacs equation. By extending the stochastic Perron’s method to our setting, we show that the value function of the problem is the unique viscosity solution to the resulting integro-partial HJBI equation. Joint work with Haoze (William) Yan, UC Berkeley.

Sara Mazzonetto (Université de Lorraine)

Title: Sticky interfaces and local time approximation

Abstract: We study diffusion processes on the real line that slow down when they hit a special point. At this point, there is a stickiness phenomenon. The simplest example of such processes is sticky Brownian motion. The time spent at the sticky point can be estimated from discrete observations using local time approximations, for instance by counting the number of crossings. Stickiness changes the convergence rates and limiting distributions compared to standard Brownian motion, highlighting its impact on statistical analysis of diffusions. This talk is partially based on joint works with A. Anagnostakis (IECL Metz).

Sergey Nadtochiy (Carnegie Mellon University)

Title: Second order mean-curvature flow as a mean-field game

Abstract: The celebrated mean-curvature flow describes the evolution of the interface between two domains which moves so that its orthogonal velocity at each point is proportional to its mean curvature, pointing in the direction of decreasing the curvature. In the second order mean-curvature flow, it is the derivative of the orthogonal velocity (i.e., the acceleration) that is proportional to the mean curvature. Both flows can be described through partial differential equations (PDEs) for the associated arrival time functions. However, unlike the PDE for the classical mean-curvature flow, the equation for its second order version — which we refer to as the `cascade equation” — is hyperbolic and does not enjoy the comparison principle. For this reason, and due to other challenges, the standard PDE tools are not sufficient to develop a well-posedness theory for the cascade equation directly. Nevertheless, it turns out that solutions to the cascade PDE can be identified with minimal elements of a set of value functions in a family of mean-field games. As a result, the existence of a solution to the cascade equation can be shown by proving the compactness of the aforementioned set of value functions, which we accomplish by employing the tools from Geometric Measure Theory. Joint work with Y. Guo and M. Shkolnikov.

Pedro Pérez-Aros (Universidad de Chile)

Title: Chance-Constrained Optimization and Spherical Radial Decomposition

Abstract: Chance-constrained optimization problems are a fundamental class of models within stochastic programming, used to handle decision-making under uncertainty. These problems involve minimizing an objective function subject to probabilistic constraints that ensure feasibility with high confidence. Formally, they can be expressed as the minimization of a function over a feasible set defined by constraints of the form $\mathbb{P}(g(x, \xi) \leq 0) \geq p$, where $\xi$ is a random vector and $p \in (0,1)$ denotes the required probability level. Despite their modeling relevance in fields such as finance, energy, and engineering, chance-constrained problems are often computationally challenging due to the non-convexity and intractability of the underlying probability function. In particular, when the function $g(x,\xi)$ is nonlinear in $\xi$, a reduction to known distribution functions is no longer possible. In such cases, the so-called spherical-radial decomposition offers a promising alternative for computing not only function values but also derivatives. In this talk, we introduce this decomposition and demonstrate how it has contributed over the past decade to advancing both the theoretical understanding and the numerical resolution of this class of problems. We highlight its role in developing efficient algorithms and establishing stability results under empirical approximations.

Joshué Ricalde (ETH Zürich)

Title: From Particles to Mean-Field to Quantum Systems: Operator-Valued Non-Commutative Probability Methods for the Propagation of Chaos

Abstract: On one hand, the theory of Mean-Field Games studies the behavior of large interacting particle systems in which individual influences weaken as the population grows. On the other, Operator-valued Free Probability investigates the asymptotic behavior of ensembles of random block-matrix models in the large-dimension limit. Both frameworks are motivated by physics—statistical mechanics for Mean-Field Games and quantum field theory for Operator-valued Free Probability—and both share a common goal: understanding emergent collective phenomena from complex microscopic interactions. In this talk, we propose a framework that combines these perspectives, using non-commutative operator-valued stochastic analysis to study particle systems with many participants. This is joint work with Prof. Dr. Dylan Possamaï.

Andrés Riveros (Columbia University)

Title: Quadratically Regularized Optimal Transport

Abstract: The quadratically regularized optimal transport problem (QOT) has emerged in the literature as a sparse alternative to the celebrated entropically regularized transport problem (EOT). Unlike EOT, whose solutions always have full support—even for small regularization parameters—QOT solutions, or QOT plans, tend to approximate the support of the unregularized transport problem, which concentrates on the graph of a function under mild conditions. This gives way to some natural questions that I will intend to answer in this talk, such as: Why do we care about sparsity? How does this sparsity manifest, and is it monotone? Can we efficiently approximate QOT? This is joint work with my co-advisor Marcel Nutz and Dr. Alberto González-Sanz.

Scott Robertson (Boston University)

Title: Rational Expectations Equilibrium with Endogenous Information Acquisition Time

Abstract: In this talk, we establish equilibrium in the presence of heterogeneous information. In particular, there is an insider who receives a private signal, an uninformed agent with no private signal, and a noise trader with semi price-inelastic demand. The novelty is that we allow the insider to decide (optimally) when to acquire the private signal. This endogenizes the entry time and stands in contrast to the existing literature which assumes the signal is received at the beginning of the period. Allowing for optimal entry also enables us to study what happens before the insider enters with private information, and how the possibility for future information acquisition both affects current asset prices and creates demand for information related derivatives. Results are valid in continuous time, when the private signal is a noisy version of the assets’ terminal payoff, and when the quality of the signal depends on the entry time. This is joint work with Jerome Detemple of Boston University.

Terry Rockafellar (University of Washington)

Title: Stochastic Divergences in Understanding Risk and Information

Abstract: The information theory of Bolzmann and Shannon is dominated by Kullback-Leibler divergence as the reverse of entropy, but stochastic divergences, which give distances of a sort from one probability distribution to another, have a much bigger role to play than that. Wasserstein divergences, associated with optimal transport, are popular now in schemes of machine learning, and phi-divergences are used in creating uncertainty sets in so-called distributionally robust optimization. All this fits into a broader picture of risk theory and its duality underpinnings in convex analysis.

Marco Rodrigues (ETH Zürich)

Title: Robust Hedging of American Options via Aggregated Snell Envelopes

Abstract: We construct an aggregator for a family of Snell envelopes in a nondominated framework. We apply this construction to establish a robust hedging duality, along with the existence of a minimal hedging strategy, in a general semi-martingale setting for American-style options. Our results encompass continuous processes, or processes with jumps and non-vanishing diffusion. A key application is to financial market models, where uncertainty is quantified through the semi-martingale characteristics.

Mateo Rodriguez (ETH Zürich)

Title: Information Leakage and Opportunistic Trading Around the FX Fix

Abstract: When dealers hedge large currency fix exposures on behalf of their clients, this can lead to predictable price patterns that opportunistic traders can exploit. We show that the cost of this information leakage is predominantly borne by the client, but that it can be partially mitigated when the dealer hedges some of their exposure ahead of the fixing window. The dealer also benefits from such a strategy because it lets them average in at a hedging price that is favourable compared to where the fix is expected to settle. Information leakage therefore mitigates a conflict of interest that would otherwise exist by aligning the interests of the dealer and the client against those of the opportunistic trader.

Mathieu Rosenbaum (École Polytechnique)

Title: Core Order Flow: The Invisible Hand of Market Dynamics

Abstract: We introduce a joint microfoundation for volatility and order flow that is consistent with salient empirical facts. In particular, it identifies the so-called core order flow as the latent driver underlying the main statistical regularities of financial markets. We start from a two-layer Hawkes framework that separates core activity, representing non-reactive trading rooted in long-term information, from reaction activity, capturing endogenous responses to observed trades. In the natural continuous time limit of this model, volatility (and the unsigned order flow) is rough but the signed order flow is a mixture of a smooth process with long-range dependence and a martingale. In addition, under no-arbitrage constraints, the model endogenously connects the exponents governing order flow, volume, market impact and volatility.

Chiara Rossato (ETH Zürich)

Title: Time-inconsistent stochastic games with mean-variance preferences

Abstract: We investigate a time-inconsistent N-player game in continuous time, where each player’s objective functional depends non-linearly on the expected value of the state process, including classic mean-variance models as a special case. We identify subgame-perfect Nash equilibria and characterise each player’s value function using a system of coupled backward stochastic differential equations. Building on this, we further analyse the mean-field counterpart and its associated mean-field equilibria.

Alexandros Saplaouras (ETH Zürich)

Title: Stability of Backward Propagation of Chaos and Numerical Approaches

Abstract: We study the asymptotic behavior of mean-field systems of backward stochastic differential equations with jumps (BSDEs). As the number of interacting equations tends to infinity, their solutions converge to independent and identically distributed copies of the limiting McKean–Vlasov BSDE (MVBSDE), a phenomenon known as backward propagation of chaos. We establish a general framework ensuring that this property is preserved, in both discrete- and continuous-time settings. Finally, we discuss numerical approximation approaches for (MV-)BSDEs based on neural network techniques, and we present some results for specific cases.

Stefan Schrott (Universität Wien)

Title: Brenier’s theorem for adapted transport II

Abstract: We develop Brenier theorems on iterated Wasserstein spaces. For a separable Hilbert space $H$ and $N\ge 1$, we construct a full-support probability $\Lambda$ on $\mathcal{P}_2^{N}(H)= \Pc_2(\ldots \Pc_2(\H)\ldots)$ that is transport regular: for every $Q$ with finite second moment, transporting $\Lambda$ to $Q$ with cost $\W_2^2$ admits a unique optimizer, and this optimizer is of Monge type. The analysis rests on a characterization of optimal couplings on $\mathcal{P}_2(H)$ and, more generally, on $\mathcal{P}_2^{\,N}(H)$ via convex potentials on the Lions lift; in the latter case we employ a new adapted version of the lift tailored to the $N$-step structure. A key idea is a new identification between optimal-transport $c$-conjugation (with $c$ given by maximal covariance) and classical convex conjugation on the lift.

A primary motivation comes from the adapted Wasserstein distance $\AW_2$: our results yield a first Brenier theorem for $\AW_2$ and characterize $\AW_2^2$-optimal couplings through convex functionals on the space of $L_2$-processes.

This is joint work with Mathias Beiglböck and Gudmund Pammer.

Francisco Silva (Université de Limoges)

Title: Approximation and perturbations of stable solutions to mean field game systems

Abstract: In this talk we present a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we present our main results on a simple stationary case. We propose an abstract framework to study these solutions by reformulating the mean field game system as an abstract equation in a Banach space. In this context, stable equilibria turn out to be regular solutions to this equation, meaning that the linearized system is well-posed.

Ludovic Tangpi (Princeton University)

Title: Particle system approximation of Nash equilibria in large games

Abstract: We develop a probabilistic framework to approximate Nash equilibria in symmetric N-player games in the large population regime, via the analysis of associated mean field games (MFGs). The approximation is achieved through the analysis of a McKean-Vlasov type Langevin dynamics and their associated particle systems, with convergence to the MFG solution established in the limit of vanishing temperature parameter. Relying on displacement monotonicity or Lasry-Lions monotonicity of the cost function, we prove contractility of the McKean-Vlasov process and uniform-in-time propagation of chaos for the particle system. Our results contribute to the general theory of interacting diffusions by showing that monotonicity can ensure convergence without requiring small interaction assumptions or functional inequalities. The talk is based on join work with N. Touzi (NYU).

Josef Teichmann (ETH Zürich)

Title: Geometric Aspects of generative AI with some applications to time series generation

Abstract: We consider forward and backward hypo-elliptic diffusion processes for the purpose of sampling from data with a geometric structure. Insights are applied to time series generation in Finance. (joint work with Fenghui Yu).

Mariano Vazquez (Universidad de Chile)

Title: Cyber risk prevention under risk averse spectral criteria

Abstract: This work introduces a model for the prevention and mitigation of cyber risks in networked systems using a risk-averse approach based on spectral criteria. An initial graph is subject to external cyber attacks, modeled by a Susceptible-Infected-Susceptible (SIS) Markov process with controlled infection and recovery rates. We consider the problem of minimizing the risk associated with the evolving structure of the network by employing self-protection and self-insurance efforts, as well as purchasing insurance coverage. We introduce spectral criteria—dependent on the eigenvalues of the graph Laplacian at final time T—for which we establish monotonicity in the sense of first‐order stochastic dominance and continuity with respect to the Wasserstein distance. This framework enables us to prove the existence of minimizers for two general optimization problems under consideration: the cases of global and local self-protection. We illustrate our theoretical findings by numerical simulations.

Benjamín Vera (Universidad de Chile)

Title: Contributions to the Existence and Computation of Nash Equilibria in Electricity Markets with Pollution Constraints

Abstract: This work presents a multi-leader-single-follower game-theoretic model of a decentralized electricity market, structured around an Independent System Operator (ISO) and incorporating quadratic transmission losses, nodal pricing, and pollution constraints. On the theoretical side, the ISO’s response to strategic agent bids is shown to be well-posed and continuously differentiable under mild assumptions, which enables the formulation of a tractable mixed complementarity problem (MCP) for computing candidate market equilibria. A preliminary discussion on existence of solutions—in both the pure and the mixed strategy sense—is also included. A numerical strategy based on grid search and solution verification is developed to identify valid Nash equilibria from MCP solutions. The method is implemented in the GAMS modeling framework using the KNITRO and GUROBI solvers, and applied to several test instances, including one inspired by the Chilean electricity network. Through numerical sensitivity analysis, the impacts of two pollution control mechanisms—pollution cost and pollution limits—are evaluated in terms of their effects on energy mix, nodal prices, pollution emissions, and ISO operating cost. The findings highlight complex trade-offs between environmental regulation and market behavior in imperfectly competitive settings, and emphasize the potential for cleaner technologies to enter the market under appropriate policy design.

Matías Vera (ETH Zürich)

Title: Investment and operational planning for an electric market with path-sample constraints

Abstract: In this talk, we present a joint problem in which a centralized entity, called the Independent System Operator (ISO), intends to minimize the joint cost of operation and investment in a network structure. The problem is formulated through operational and investment control variables; we discuss the hierarchy between them and use the so-called Day Ahead Problem to find an explicit form of the optimal operational variable, which allows us to reformulate the problem as a stochastic control problem with state constraints. We extend results of state-constrained stochastic control to fit our setting. Particularly, we use a version of the Pointing Inward Condition to fully characterize the value of the problem as the unique viscosity solution of a constrained HJB equation. We then assign a specific dynamic to the capacity-demand process and discuss how the assumptions for the HJB characterization result in a budget constraint for the planning. Finally, we run simulations for a three node setting, that resembles the Chilean market, for short-term planning and long-term planning.

Emilio Vilches (Universidad de O’Higgins)

Title: Stochastic Sweeping Processes for Nonconvex Sets

Abstract: In this talk, we present recent results on the existence of solutions to stochastic sweeping processes. We discuss their connection with reflected Brownian motion and provide an application to crowd motion. This is joint work with Juan Garrido (Universidad de Chile) and Nabil Kazi-Tani (Institut Élie Cartan de Lorraine).