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Peter Bank
Title: Optimal execution and speculation with trade signals
Abstract: We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity process which reflects the balance of the demand and supply of liquidity. Limit and market orders mutually excite each other so that liquidity is mean reverting. We use the theory of Meyer-$\sigma$-fields to introduce a short-term signal process from which a trader learns about imminent changes in order flow. Her trades impact the market through the same mechanism as other orders. A novel version of Marcus-type SDEs allows us to efficiently describe the intricate timing of market dynamics at moments when her orders concur with others. In this setting, we examine an optimal execution problem and derive the Hamilton--Jacobi--Bellman (HJB) equation for the value function. The HJB equation is solved numerically and we illustrate how the trader uses the signal to enhance the performance of execution problems and to execute speculative strategies. This is joint work with Alvaro Cartea and Laura Körber.
Anna Battauz
Title: American options with liquidation penalties
Abstract: This talk explores the integration of liquidation costs into the valuation framework for American options within an arbitrage-free and otherwise frictionless market. The introduction of liquidation penalties changes the comparison between immediate payoff and continuation value for American option holders. Without these penalties, the continuation value is equal to the actual funds obtainable by selling the option. When the sale proceeds achievable upon liquidation are lower due to penalties, immediate exercise becomes more advantageous, leading to a wider optimal early exercise region. We start studying the impact of liquidation penalties in discrete time. In the continuous-time lognormal model, we derive closed-form asymptotic solutions near maturity for the critical price that triggers optimal early exercise. We also provide explicit pricing formulas for perpetual American options with liquidation penalties. Our results are relevant for executive stock options (ESOs), which typically exhibit liquidation penalties, and for the American equity options for which there is evidence of liquidation costs. Based on joint work with M. De Donno and A. Sbuelz.
Fabio Bellini
Title: Disappointment Concordance and Duet Expectiles
Abstract: We introduce an axiom of disappointment-concordance (disco) aversion for a preference relation over acts in an Anscombe-Aumann setting. This axiom means that the decision maker, facing the sum of two acts, dislikes the situation where both acts realize simultaneously as disappointments. Our main result is that, under strict monotonicity and continuity, the axiom of disco aversion characterizes preference relations represented by a new class of functionals belonging to the Gilboa-Schmeidler family, which we call the duet expectiled utilities. When the outcome space is the real line, a duet expectiled utility becomes a duet expectile, which involves two endogenous probability measures. It further becomes a usual expectile, a statistical quantity popular in regression and risk measures, when these two probability measures coincide. We discuss properties of duet expectiles and connections with fundamental concepts including probabilistic sophistication, risk aversion and uncertainty aversion. Joint work with F. Maccheroni, T. Mao, R. Wang and Q. Wu.
Fulvia Confortola
Title: Progressive Enlargement of Filtrations and Control Problems for Step Processes
Abstract: In the present work we address stochastic optimal control problems for a step process X under
a progressive enlargement of the filtration.
We denote by F the filtration generated by X: This filtration represents the information available in a market in which an agent (i.e., the controller) handles. We progressively enlarge F to G by a random time τ, that can be regarded as the occurrence time of an external shock event, as the death of the agent (e.g., life insurance) or the default of part of the market (e.g., credit risk).
We then study two related classes of control problems.
The first one consists in optimization problems over [0,T]. They can be regarded as control problems of an insider trader who has private information on τ, that is, she can use G-predictable controls. Moreover, the control problem over [0,T] allows to consider terminal costs which may depend on the default time τ, i.e., defaultable costs, for example of the form g = g_11_{τ>T} + g_21_{τ≤T}. It is evident that the associated control problem cannot be solved in the reference filtration F because the random variable g is G_T -measurable but not F_T -measurable, in general.
The second class of control problems we look at is over the random horizon [0,T ∧τ]. These can be understood as control problems of an agent who only disposes of the information available in the market, that is, she only uses F-predictable controls but, for some reasons, she has exclusively access to the market up to τ.
We solve these control problems following a dynamical approach based on a class of BSDEs driven by the jump measure in the enlarged filtration G.
Marzia de Donno
Title: Short rate models with stochastic discontinuities: a PDE approach
Abstract: In the ongoing reform of interest rate benchmarks, risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. or the Euro Short-Term Rate (eSTR) in Europe, play a pivotal role. An observed characteristic of RFRs is the occurrence of jumps and spikes at regular intervals, due to regulatory and liquidity constraints. In this paper, we consider a general short-rate model featuring discontinuities at fixed times with random sizes. Within this framework, we introduce a PDE-based approach to price interest rate derivatives. For affine models, we derive (quasi) closed-form solutions, while for the general case, we develop numerical methods to solve the resulting PDEs.
Alessandro Doldi
Title: Collective arbitrage and dynamic risk measures
Abstract: We introduce the notions of Collective Arbitrage and of Collective Super-replication in a discrete-time setting where agents are investing in their markets and are allowed to cooperate through exchanges. We accordingly establish versions of the fundamental theorem of asset pricing and of the pricing-hedging duality. A reduction of the price interval of the contingent claims can be obtained by applying the collective super-replication price. We then explore the implications of cooperation on dynamic risk measurement, focusing particularly on aggregation and time consistency.
Sigrid Källblad
Title: Optimal adaptive control using Measure-valued martingales
Abstract: We consider an `optimal adaptive control problem' where the aim is to optimally steer a noisy observation in order to minimise some cost functional depending on a hidden signal. We show that this problem admits an equivalent weak formulation and that the solution can be characterised in terms of an HJB equation. Our approach is based on exploiting viscosity theory for controlled MVMs to tackle the problem. Based on joint work with Alex Cox and Chaorui Wang.
Athena Picarelli
Title: A finite-dimensional numerical scheme for extended mean-field control problems
Abstract: We present a finite-dimensional numerical approximation scheme for a class of extended mean field control (MFC) problems. Our algorithm leverages the approximation of the mean field problem by a finite-player cooperative optimisation problem, due to the propagation of chaos, together with the usage of finite-dimensional neural network solvers. This avoids the need to directly approximate functions on an infinite-dimensional Wasserstein domain, and allows for more efficient memory usage and faster computation times.
Sergio Pulido
Title: Invariance and Explosions of Stochastic Volterra Equations
Abstract: I will discuss recent invariance principles for stochastic Volterra equations (SVEs), leveraging the theory of convolution equations. In the one-dimensional case, when open sets are considered, I will present a Feller-type test for explosions under dynamics governed by nonsingular kernels. Additionally, I will introduce an Osgood criterion for explosions of SVEs with additive noise, featuring kernels from a family that includes the fractional kernel.
Nizar Touzi
Title: TBA
Abstract: TBA
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