Volker Krätschmer (University of Duisburg-Essen)
Titel: Minimax theorems for American options without time-consistency
Abstract: In the talk we shall present sufficient conditions guaranteeing validity of the well-known minimax theorem for the lower Snell envelope. Such minimax results play an important role in the characterisation of arbitrage-free prices of American contingent claims in incomplete markets. Our conditions do not rely on the notions of stability under pasting or time-consistency and reveal some unexpected connection between the minimax result and path properties of the corresponding density process. We shall exemplify our general results in the case of families of measures corresponding to diffusion exponential martingales with some substantial refinements obtained recently. At the end of the talk we shall discuss how to extend the minimax results to the model free situation where no reference probability measure is given in advance. The talk is based on a joint work with Denis Belomestny, Tobias Hübner and Sascha Nolte.
Renyuan Xu (Hooke Research Fellow, University of Oxford)
Titel: A Case Study on Pareto Optimality for Collaborative Stochastic Games
Abstract: Pareto Optimality (PO) is an important concept in game theory to measure global efficiency when players collaborate. In this talk, we start with the PO for a class of continuous-time stochastic games when the number of players is finite. The derivation of PO strategies is based on the formulation and analysis of an auxiliary N-dimensional central controller?s stochastic control problem, including its regularity property of the value function and the associated Skorokhod problem. This PO strategy is then compared with the set of (non-unique) NEs strategies under the notion of Price of Anarchy (PoA). The upper bond of PoA is derived explicitly in terms of model parameters. Finally, we characterize analytically the precise difference between the PO and the associated McKean-Vlasov control problem with an infinite number of players, in terms of the covariance structure between the optimally controlled dynamics of players and characteristics of the no-action region for the game. This is based on joint work with Xin Guo (UC Berkeley).
Umut Centin (London School of Economics)
Titel: Equilibrium in limit order markets
Abstract: Building upon the setting of Glosten (1994) we study equilibrium among limit order traders and multiple informed investors where the market clearance is provided by dealers. In a one-period model we establish the existence of equilibrium by solving a fixed-point problem and study the impact of model parameters on the bid-ask spread and trading costs. Even in the absence of explicit solutions, the model allows us to compute the asymptotics of trading costs. We show that the price impact follows a power or logarithmic function depending on whether the distribution of the fundamental value of the traded asset has heavy tails or not.
Joint work with Henri Waelbroeck.
Julio Backhoff Veraguas (University of Twente)
Titel: All adapted topologies are equal
Abstract: Several researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes (ie. filtrations). We find that all of these seemingly independent approaches define the same topology in finite discrete time. Moreover, we explain how optimal transport theory can be used to obtain a compatible metric that is both tractable and highly relevant for a number of practical questions. (Based on joint works with D. Bartl, M. Beiglboek, M. Eder.)
Mitja Stadje (University of Ulm)
Titel: Hedging under permanent market impacts
Abstract: We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. In contrast to the standard framework of financial engineering, a trader is no more price taker as any trade has a permanent market impact via an effect to the supplier?s inventory. The P&L of a trading strategy is written as a nonlinear stochastic integral. We consider some stochastic optimal control problems and give connections to several branches of stochastic analysis
René Aid (University of Paris Dauphine)
Titel: Optimal electricity demand response contracting with responsiveness incentives
Abstract: Despite the success of demand response programmes in retail electricity markets in reducing average consumption, the random responsiveness of consumers to price event makes their efficiency questionable to achieve the flexibility needed for electric systems with a large share of renewable energy. This paper aims at designing demand response contracts which allow to act on both the average consumption and its variance.
The interaction between a risk--averse producer and a risk--averse consumer is modelled as a Principal-Agent problem, thus accounting for the moral hazard underlying demand response contracts. The producer, facing the limited flexibility of production, pays an appropriate incentive compensation to encourage the consumer to reduce his average consumption and to enhance his responsiveness. We provide closed--form solution for the optimal contract in the linear case. We show that the optimal contract has a rebate form where the initial condition of the consumption serves as a baseline and where the consumer is charged a price for energy and a price for volatility. The first--best price for energy is a convex combination of the marginal cost and the marginal value of energy where the weights are given by the risk--aversion ratios, and the first--best price for volatility is the risk--aversion ratio times the marginal cost of volatility. The second--best price for energy and volatility are decreasing non--linear function of time inducing decreasing effort. The price for energy is lower (resp. higher) than the marginal cost of energy during peak--load (resp. off--peak) periods.
We illustrate the potential benefits issued from the implementation of an incentive mechanism on the responsiveness of the consumer by calibrating our model with publicly available data.
Joint work with Dylan Possamaï (Columbia University) and Nizar Touzi (Ecole Polytechnique).