Erhan Bayraktar

Title. Equilibrium transport with time-inconsistent costs: an application to matching problems in the job market.

Abstract. Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences under a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized optimal transport with general f-divergence. Under the bi-causal constraint, we introduce the concept of equilibrium transport and provide a characterization. We apply our framework to study inertia of two job markets, top-ranking executives and academia. The empirical analysis shows that a job market with stronger inertia is less efficient. The University of California (UC) postdoc job market has the strongest inertia even than that of executives, while there is no evidence of inertia in the UC faculty job market. Joint work with Bingyan Han. 

Jean-Francois Chassagneux

Title. A dual approach to partial hedging.

Abstract. We introduce a class of `weak hedging problem’ which contains as special examples the quantile hedging problem (Föllmer Leukert 1999) and PnL matching problem (introduced in Bouchard & Vu 2012). We show that they can generally be rewritten as a kind of Monge transport problem. Using this observation, we introduce a Kantorovich version of the problem and, in some cases, we are able to prove a dual formulation. This allows us to design numerical methods based on SGD algorithms to compute the weak hedging price. This is a joint work with C. Bénézet (ENSIIE) and M. Yang (Université Paris Cité).

Ibrahim Ekren

Title. Monge-Kantorovich duality, informed trading, and risk aversion.

Abstract. We establish a novel connection between optimal transport theory and the dynamic version of the Kyle model of informed trading. Our methodology based on the Monge-Kantorovich duality and backward stochastic partial differential equations allows us to obtain the existence of equilibrium in all risk-neutral versions of the model studied in the literature and extend the existence results to novel cases. With risk-averse market makers, we show that liquidity is lower, assets exhibit short-term reversals, and risk premia depends on market maker inventories, which are mean reverting. We illustrate the model by showing that implied volatilities predict stock returns when there is informed trading in stocks and options and market makers are risk averse. Based on joints work with K. Back, S.Bose, R. Chhaibi, F. Cocquemas, A. Lioui, E. Noh, and L. Vy.

Paolo Guasoni

Title. Lightning network Economics: channels and topology

Abstract. Designed to address Bitcoin’s scalability challenge, the Lightning Network (LN) is a protocol allowing two parties to secure bitcoin payments and escrow holdings between them. In a lightning channel, each party commits collateral towards future payments to the counterparty and payments are cryptographically secured updates of collaterals. First, we identify conditions for two parties to optimally establish a channel, find explicit formulas for channel costs and optimal collaterals, and derive the implied reduction in congestion of the blockchain. Then we obtain necessary conditions for cost-minimizing topologies and bounds on the cost of the optimal topology, showing the unusual circumstances in which it is a hub that connects all other nodes.

Emma Hubert

Title. Continuous-time incentives in hierarchies.

Abstract. In this talk, we will study a model of continuous–time optimal contracting in a hierarchy, which generalizes the one-period framework of Sung (2015). The hierarchy is modelled by a series of interlinked principal-agent problems, leading to a sequence of Stackelberg equilibria. More precisely, the principal (she) can contract with a manager (he), to incentivize him to act in her best interest, despite only observing the net benefits of the total hierarchy. The manager in turn subcontracts the agents below him. We will see through a simple example that, while the agents only control the drift of their outcome, the manager controls the volatility of the Agents’ continuation utility. Therefore, even this relatively simple introductory example justifies the use of recent results on optimal contracting for drift and volatility control, and therefore the theory on 2BSDEs. We will also discuss some possible extensions of this model, in particular when the outcome processes can be impacted by negative random jumps, representing accidents, and the workers can control their intensity. Joint work in progress with Sarah Bensalem and Nicolas Hernandez-Santibanez.

Tomoyuki Ichiba

Title: Smoothness of directed chain stochastic differential equations and its applications.

Abstract: On a filtered probability space for the space of continuous functions, we shall consider a system of stochastic equations called directed chain stochastic differential equations for a pair of stochastic processes whose marginal distributions in the path space are identical and their joint distribution is uniquely determined by the system of equations with the distributional constraints.  In this talk we discuss the smoothness of the solutions of the equations under some regular conditions first, and then consider some relaxation of the conditions on the coefficients and the distributional constraints. We also introduce its applications of such systems in the stochastic filtering problem and in the generative adversarial network problem.

Martin Larsson

Title. Controlled measure-valued martingales: a viscosity solution approach
Abstract. We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs). We establish the `classical' results of stochastic control for these problems: specifically, we prove that the value function for the problem can be characterised as the unique solution to the Hamilton-Jacobi-Bellman equation in the sense of viscosity solutions. In order to prove this result, we exploit structural properties of the MVM processes. Our results also include an appropriate version of Itô's lemma for controlled MVMs. We also show how problems of this type arise in a number of applications, including model-independent derivatives pricing, the optimal Skorokhod embedding problem, and two player games with asymmetric information. (Joint work with Alex Cox, Sigrid Källblad, and Sara Svaluto-Ferro.)

Oleksii Mostovyi

Title. Pricing of contingent claims in large markets.

Abstract. We consider the problem of pricing in large markets in a framework where the large market limits the small ones with finitely many traded assets. We show that this framework allows accommodating indifference pricing in stochastic utility settings and arbitrage-free pricing. Adopting a stochastic integration theory with respect to a sequence of semimartingales, we introduce the notion of indifference prices for the large post-limit market and establish their existence, uniqueness, and relation to arbitrage-free prices. These results rely on a theorem of independent interest on utility maximization with a random endowment in a large market that we state and prove first. Further, we provide approximation results for the indifference and arbitrage-free prices in the large market by those in small markets. In particular, our framework allows for pricing the asymptotically replicable claims, where we also show a consistency of the pricing methodologies and provide positive examples. This talk is based on the joint work with Pietro Siorpaes.

Johannes Muhle-Karbe

Title: The cost of misspecifying price impact.

Abstract: Portfolio managers’ orders trade off return and trading cost predictions. Return predictions rely on alpha models, whereas price impact models quantify trading costs. We study what happens when trades are based on an incorrect price impact model, so that the portfolio either over- or under-trades its alpha signal. We derive tractable formulas for these misspecification costs and illustrate them on proprietary trading data. (Joint work in progress with Jean-Philippe Bouchaud, Natascha Hey, Iacopo Mastromateo and Kevin Webster.)

Marcel Nutz

Title: Unwinding stochastic order flow in a central risk book.

Abstract: We study the optimal execution problem for the Central Risk Book (CRB), a centralized trading unit recently established in many large banks and trading companies. The CRB aggregates orders from the other business units within the organization in real time, netting opposite orders and executing outstanding orders such as to minimize transaction costs. Thus, the in-flow orders of the CRB are a stochastic process. We introduce a tractable model for the price impact and spread cost paid by the out-flow orders and find the optimal execution strategy for a general class of in-flow processes. The strategy highlights how future in-flows are taken into account to determine the optimal trade-off between trading speed and transaction costs. (Joint work with Kevin Webster and Long Zhao.)

Dylan Possamai

Title: Moral hazard for time-inconsistent agents, BSVIEs and stochastic targets.
Abstract: We address the problem of Moral Hazard in continuous time between a Principal and an Agent that has time-inconsistent preferences. Building upon previous results on non-Markovian time-inconsistent control for sophisticated agents, we are able to reduce the problem of the principal to a novel class of control problems, whose structure is intimately linked to the representation of the problem of the Agent via a so-called extended Backward Stochastic Volterra Integral equation. We will present some results on thecharacterisation of the solution to problem for different specifications of preferences for both the Principal and the Agent, and relate the general setting to control problems with Volterra stochastic target constraints.

Adrien Richou

Title: BSDEs reflected in a non-convex domain: geometry strikes back.

Abstract: In a recent paper, we have proved, with J.-F. Chassagneux and S. Nadtochiy, some existence and uniqueness results for BSDEs reflected in a non-convex domain under some restrictive assumptions on the domain and the terminal condition. All these results were obtained by tools and estimates based on the Euclidean structure of $\mathbb{R}^d$. In order to improve these results, at least in dimension $2$, it is also possible to see our domain as a flat manifold with a boundary and to take advantage of geometry tools already developed to tackle martingales in (non flat) manifolds (without boundary). In this talk, I will explain this new approach and the kind of results we are able to obtain. This is a work in progress with M. Arnaudon, J.-F. Chassagneux and S. Nadtochiy.

Scott Robertson

Title: Equilibrium with asymmetric information and general uninformed agent preferences.

Abstract: In this talk, we establish the existence of equilibrium in the presence of both asymmetric information and general preferences for the uninformed agent. Specifically, there is an insider who possesses a private signal about the terminal value of the traded asset, and an uninformed agent who possesses no private signal. While the insider has CARA (exponential) preferences, the uninformed agent’s preferences are described by a general utility funtion defined on $(0,\infty)$ . The terminal value of the traded asset is a function of a time homogenous diffusion. In this setting, and under mild conditions on the diffusion, terminal payoff function, and uninformed preferences, we establish existence of a partially revealing equilibrium, where a market signal is communicated to all agents at time zero. Additionally, the equilibrium is a rational expectations equilibrium in the univariate case. As the uninformed agent preferences are general, we are able to obtain sensitivity of the asset price, volatility, and market price of risk, to the uninformed agent’s initial endowment, as we will show through examples. This is joint work with Jerome Detemple of Boston University.

Mathieu Rosenbaum

Title. Understanding the role of participation rate in the square root law.
Abstract. The square root law of market impact is now a well admitted statistical feature of financial transactions. It states that a metaorder of volume Q generates on average a price deviation of magnitude square root of Q. Several approaches in the literature provide microstructural foundations for this phenomenon so that we are now quite close to a good understand of this property. When giving a closer look at empirical data, one however realizes that the pre-factor in front of square root is actually a concave function of the participation rate. In this talk we provide a trading-based explanation for this intriguing statistical property. We recover in particular the crossover phenomenon observed in Bucci et al. This is joint work with Bruno Durin and Grégoire Szymanski.

Jianfeng Zhang

Title: Voting with decentralized policy contingent payment promises.

 Abstract: We examine a model where a committee adopts or rejects a reform based on voting. Committee members have heterogeneous intensities of preferences for the reform, with some of them supporting it and others opposing it. The reform is efficient because it generates the largest aggregate preference intensities. Prior to voting, committee members can freely make enforceable utility transfer promises that are contingent on the committee’s decision. The promises can involve coalitions of any size ranging from a pair to the entire committee. We define equilibrium promises by 1) precluding the blocking coalitions which members can make Pareto improving internal promises and lead the group to reject the reform and, 2) minimizing the aggregate transfer promises. We find that equilibrium promises exist and are indeterminate, but do share several key characteristics. First, all equilibria require top-down promises from members with high preference intensity to members with low preference intensity for the reform. Second, when the coalition opposing the reform is large enough to induce the group to reject the reform, transfer promises restore efficiency. The promises enable the committee to adopt the reform because members of the minority coalition supporting it compensate members of the complementary majority coalition to entice them to vote for the reform. Inefficiencies resulting from voting externalities are thus removed. Third, when the committee adopts the reform because the coalition supporting it is large enough, promises may be required to preempt members of the losing coalition opposing the reform from enticing the least intense members of the coalition supporting the reform into voting against it and reversing the committee decision. The talk is based on a joint work with Ali Lazrak.

Yuchong Zhang

Title: A mean field game of sequential testing.

Abstract: We introduce a mean field game of optimal stopping with filtering. Specifically, we analyze the sequential testing of a common Brownian drift where the stopping decision of all agents collectively affects their private signal processes. Under suitable conditions, we show that the game is well-posed and establish the existence of a Nash equilibrium. (Joint work with Steven Campbell).

Gordan Zitkovic

Title: Kyle's model with stochastic liquidity.

Abstract: We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our equilibrium allows us to study the impact of the stochastic volatility of noise trading on the volatility of the asset. In particular, when the fundamental price is log-normally distributed, informed trading forces the log-return up to maturity to be Gaussian for any choice of noise-trading volatility even though the price process itself comes with stochastic volatility. Surprisingly, we find that in equilibrium both Kyle's Lambda and its inverse (the market depth) are submartingales. Joint work with Ibrahim Ekren and Brad Mostowski.