Titles and Abstracts
Ben Hambley
Title: Systemic risk, endogenous contagion and Mckean-Vlasov control
Abstract: TBC
John Moriarty
Title: Iterated majorants: representations for multidimensional optimal stopping
Abstract: We construct the least superharmonic majorant of a continuous function $g$ on the $d$-dimensional unit ball ($d\ge 2$) by a canonical iteration of harmonic envelopes. This yields an explicit pointwise approximation scheme with no classical counterpart and provides a multidimensional analogue of the Dynkin--Yushkevich concave-envelope representation for the value function of an optimal stopping problem. Probabilistically, the iteration corresponds to successive compositions of stopping times and overcomes the localisation obstruction arising from the thinness of Brownian paths in dimensions $d\ge 2$. The representation is established under a Lipschitz regularity condition on the constructed majorant. We show how Mobius transformations generate an infinite-dimensional family of explicit non-radial examples in the plane.
Miryana Grigorova
Title: TBC
Abstract: TBC
Gechun Liang
Title: Nonzero-sum Dynkin games beyond the order condition: SWOR and convertible bonds
Abstract: We study continuous-time nonzero-sum Dynkin games beyond the order condition, under which the first-stopper payoff is dominated by the second-stopper payoff for each player. Motivated by applications such as perpetual convertible bonds, we introduce a new equilibrium concept, \emph{stopping with the opportunity to react} (SWOR), which allows the player with priority under simultaneous stopping to distinguish between voluntary stopping and contingent stopping in response to the opponent's action. Our main result shows that every SWOR equilibrium is equivalent to a stopping-time Nash equilibrium of an explicitly constructed ordered Dynkin game with modified payoff functions satisfying the order condition. As applications, we revisit the perpetual convertible bond model of [N. Chen, M. Dai and X. Wan, \emph{Math. Finance}, 23 (2013), pp.~57--93], where SWOR eliminates the Pareto-dominated equilibria admitted by the stopping-time Nash equilibrium, and introduce a sequential-conversion model in which bankruptcy threats generate endogenous low-value conversion barriers, providing a game-theoretic explanation for conversion triggers in contingent convertible bonds.
David Siska
Title: Mirror descent methods in discrete and continuous time RL
Abstract: Mirror descent (MD) is a variant of policy gradient (PG) methods that has favourable geometric properties. Thanks to these properties, MD achieves (sub)linear convergence in the population setting (i.e., assuming exact evaluation of all integrals) for many reinforcement learning (RL) applications. We focus on recent convergence results for MD-based actor-critic methods in both discrete- and continuous-time regime and discuss the gaps that remain in our understanding when neural networks are used for function approximation and only sampled data is available.
Thomas Steffen
Title: Robust and Stochastic Predictive Control of Energy Storage Systems
Abstract: This talk examines stochastic control problems arising in the transition to net-zero energy systems. Increasing shares of renewable generation introduce significant uncertainty in both electricity supply and market prices, while storage systems provide new flexibility for balancing supply and demand. The talk contrasts robust and stochastic approaches to constrained predictive control under uncertainty, using energy storage systems as a motivating application. The resulting control problems are often simple in terms of system dynamics but challenging due to the interaction of uncertainty, physical constraints, and storage losses. Focusing on grid-connected microgrids with energy storage, we consider the problem of scheduling charging and discharging decisions under uncertain future electricity prices and demand. A fundamental trade-off arises between conservative strategies that maintain larger energy reserves and more aggressive strategies that exploit the possibility of lower future prices. This trade-off can be formulated as an expected-cost optimisation problem and solved using stochastic model predictive control (SMPC). The resulting controller balances the risk of future price increases against the opportunity presented by lower future prices, while responding to unexpected disturbances. The problem becomes more challenging when uncertainty interacts with hard operational constraints, as commonly found in closed energy systems. Here, the controller must balance the cost of precautionary action against the risk of constraint violation, trading quantities that are often difficult to compare directly. Two common approaches are robust formulations based on finite uncertainty sets, such as tube MPC, and stochastic formulations that assign an explicit cost to constraint violations, leading back to SMPC. The talk highlights how these modelling choices influence both system operation and electricity market outcomes. It also shows why the combination of uncertainty, dynamics, and hard constraints remains one of the central challenges in the control of energy storage systems, and more sophisticated uncertainty models are required.
Michael Tehranchi
Title: Weighted peacock martingales: models of all vanilla claims
Abstract: Dupire (1994) famously constructed an asset price model that exactly matches the quoted prices of all vanilla contingent claims. Carmona and Nadtochiy (2009) proposed a dynamic generalisation of Dupire's model, inspired by the Heath--Jarrow--Morton framework for interest rates. This talk revisits the Carmona--Nadtochiy framework, exploring issues around existence of non-trivial solutions and discrete-time approximations.
Mihail Zervos
Title: Long-run portfolio optimisation in the presence of proportional transaction costs: equivalent risk sensitive and robust formulations
Abstract: We study long-run optimal investment with proportional transaction costs in a market comprising a money market account and a stock, under a no short-selling constraint. We consider two formulations: a risk sensitive portfolio optimisation problem, with risk sensitivity parameter $\theta$, and a robust problem in which the investor penalises deviations from a reference model by their relative entropy. We show that the two are associated with the same ergodic HJB equation, the robust problem corresponding to the risk sensitive one with $\theta$ replaced by $-\theta$. After a suitable rescaling of the controls, both problems reduce to a one-dimensional singular stochastic control problem for the fraction of wealth invested in the stock. We derive the complete solution to this control problem by constructing a $C^2$ solution to its HJB equation. The solution takes three qualitatively different forms, depending on the position of the risk sensitive analogue of the Merton fraction relative to the interval $]0,1[$. In two of these, it is optimal for the investor to move the entire portfolio value into the money market account or into the stock at time $0$ and make no trades thereafter. In the third one, it is optimal to keep the fraction of wealth invested in the stock inside an interval $[\alpha^\star, \beta^\star] \subset \mbox{} ]0,1[$ by exerting the minimal effort required to do so.
Lucas M. Moschen
Title: A Feedback-Control Perspective on Sampling for Langevin and McKean-Vlasov Dynamics
Abstract: Mean-field control defines a control law for large populations by considering a continuum model. In practice, however, only the agents are observed, rather than the density on which feedback control laws are based. We study the implementation of control at the agent level for noisy interacting agents on a periodic domain whose mean-field limit is a Wasserstein gradient flow, following our ongoing program of proving local stabilisability of any stationary state of a McKean-Vlasov PDE. Stabilisation can be achieved at any prescribed rate $\delta > 0$ at the expense of a larger, but still finite, number of control inputs. The feedback is evaluated using finitely many empirical moments and does not require density estimation, relying instead on the positions of the particles. We prove that, for initial configurations close to the target, the expected squared Wasserstein distance between the empirical measure and the target decays at any rate below the designed closed-loop spectral gap until it reaches the sampling error, and remains at this level over time horizons exponentially long in the number of agents. This guarantee persists, with an additional quadratic error, under bounded errors in the broadcast moments, bounded disturbances, and bounded model mismatch. Simulations of an unstable ring formation and bounded-confidence opinion dynamics illustrate the results, including a comparison with density feedback based on kernel density estimation.