MAFE Workshop Risk Mitigation - Abstracts
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Rene Aid
Peter Bank
Title: Optimal investment with jump signals and utility from relative performance
Abstract: We consider a model where investors receive signals on impending price jumps which allow them to adjust their positions beforehand. In the single agent case, we derive the Hamiltion-Jacobi-Bellman equation and show how its explicit solution for power utilities allows us to assess questions like when it is better to improve signal frequency than signal quality. In a multi-agent setup where utility is derived by relative performance to peers, we introduce a model where different agents receive different short-term signals and derive conditions for the existence of Nash equilibria. Numerical experiments suggest uniqueness and we discuss some behaviroal observations in this setting. The talk is based on joint work with Laura Körber and Gemma Lucia Sedrakjan.
Sara Biagini
Title: Carbon neutrality and net-zero regulation
Abstract: We analyze the impact of carbon regulation on a system of polluting companies. We consider two main compliance frameworks: one based on an ETS offset mechanism and the other relying only on abatement efforts. In a continuous time, stochastic model for the emissions, firms have to match their emissions imbalance with their reduction effort at the compliance date. Infinite dimensional scenario-wise compliance is not easy to tackle, but our methodology builds on a simple annihilation of the stochastic first-order conditions associated with the firm's individual cost minimizations. The existence and uniqueness of the optimizers and the equilibrium carbon price are proven under necessary and sufficient conditions, which are quite mild. The optimizers and the carbon price are explicit, and their analytic expression provides an instance of classic economic principles. Numerical examples illustrate the flexibility of the model and the effect of different allocation policies that may adopted by the central authority.
Jaroslav Borovicka
Title: Robust Bounds on Optimal Tax Progressivity
Abstract: We study the problem of a robust planner who designs an optimal taxation scheme for a heterogeneous population in presence of uncertainty about the shape of the distribution of underlying types. Low-income workers are well insured under the optimal scheme, and so concerns about the left tail of the type distribution are negligible. On the other hand, the planner fears misspecification of the right tail of the type distribution emerging from budgetary concerns. Even when the tail of the distribution is Pareto, arbitrarily small misspecification concerns lead to zero marginal taxes at the top. A quantitatively calibrated model shows that a plausible degree of uncertainty leads to an optimal tax scheme with substantially reduced marginal tax rates for high-income earners and a peak marginal tax rate much lower than in the model without uncertainty. Joint with Anmol Bhandari and Yuki Yao.
Samuel Cohen
Title: Risk and trading in decentralized markets
Abstract: Decentralized markets have demonstrated a variety of novel structures, leading to challenges in risk management and large scale modelling. In this talk we will discuss some examples arising in lending markets, including challenges from margin calculation, interest rate determination, and opportunities for manipulation.
Roxana Dumitrescu
Title:Energy efficiency and demand response: a mean-field game approach
Abstract:In this talk, I will present two models developed in the context of energy transition, using as mathematical tools the theory of mean-field games and the principal agent-mean-field game approach. The first model is related to demand response, in which we consider an energy system with a large number of consumers who are linked by a Demand Side Management contract, i.e. they agree to diminish, at random times, their aggregated power consumption by a predefined volume. We provide numerical results which illustrate the impact of such an interaction on the consumption and price levels. The second model focuses on the problem of an energy retailer aiming at designing a new type of contract based on a ranking system for a population of heterogeneous consumers to incentivise them to make energy economies (based on several joint works with C. Alasseur, R. Aïd, E. Bayraktar, L. Campi , Q. Jacquet, J. Zeng)
Giorgio Ferrari
Title: Exploratory Optimal Stopping: A Singular Control Formulation
Abstract: In this talk I present continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is represented by the probability of stopping within a given time--specifically, a bounded, non-decreasing, càdlàg control process. To encourage exploration and facilitate learning, we introduce a regularized version of the problem by penalizing it with the cumulative residual entropy of the randomized stopping time. The regularized problem takes the form of an (n+1)-dimensional degenerate singular stochastic control with finite-fuel. We address this through the dynamic programming principle, which enables us to identify the unique optimal exploratory strategy. For the specific case of a real option problem, we derive a semi-explicit solution to the regularized problem, allowing us to assess the impact of entropy regularization and analyze the vanishing entropy limit. Finally, we propose a reinforcement learning algorithm based on policy iteration. We show both policy improvement and policy convergence results for our proposed algorithm. The talk is based on ajoint work with Jodi Dianetti and Renyuan Xu.
Paul Hager
Title:A Mean-Field Game of Market Entry – Portfolio Liquidation with Trading Constraints –
Abstract: We consider both N-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while players with an initially long position are only allowed to sell the stock. Under suitable conditions on the model parameters we show that the games are equivalent to games of timing where the players need to determine the optimal times of market entry and exit. We identify the equilibrium entry and exit times and prove that equilibrium mean-trading rates can be characterized in terms of the solutions to a highly non-linear higher-order integral equation with endogenous terminal condition. We prove the existence of a unique solution to the integral equation from which we obtain the existence of a unique equilibrium both in the mean-field and the N-player game. Joint with Guanxing Fu and Ulrich Horst
Rüdiger Kiesel
Title:Net-Zero: Fact or Fiction
Abstract: Companies flood the public with net-zero promises, but often leave the path to net-zero unexplained or blurred. The quality of the data on carbon emissions is still insufficient and metrics for calculating carbon risks are not precisely defined. In this talk we show the deficiencies in the analysis of carbon risks and develops a methodology to capture net-zero promises and carbon risks probabilistically. As a possible application of the methodology a resilience-based approach to the regulation of financial institutions is being outlined.
Christoph Knochenhauer
Title: Utility-Based Multi-Attribute Risk Measures
Abstract: We propose a new class of monetary risk measures capable of assessing multiple sources of risk. In addition to the risk stemming from the financial exposure of a position, these measures additionally take into account a second source of risk such as the risk associated with changes in the ESG rating or carbon risk. The construction of these risk measures is based on an extension of classical shortfall risk measures in which the loss function is replaced by a multi-attribute utility function. We present an extensive theoretical analysis of these risk measures, showing in particular how properties of the utility function translate into properties of the associated risk measure. We furthermore discuss how these multi-attribute risk measures can be used to compute minimum risk portfolios and show in a numerical study that accounting for ESG risk in optimal portfolio choice can have a significant influence on the composition of optimal portfolios. This is joint work with Sebastian Geissel.
Andreas Lange
Titel: Ambiguity attitudes and surprises
Abstract: We investigate ambiguity attitudes for natural events (temperatures) and how they are updated following new information. Using a general population sample, we first obtain baseline ambiguity attitudes for future weather events based on real temperatures over several past days. Second, we study the influence of different communication types on updating the ambiguity attitudes: participants are given either point estimators, interval estimators, or the combination of both as weather forecasts. We further vary whether the forecast is surprising or in line with the initially received information. In contrast to claims that ambiguity aversion may increase in response to surprising news, we find that ambiguity attitudes are rather robust to new information and variants of their communication. Yet, different variants of communicating new information significantly change the belief updating process and affect the matching probabilities given to specific events. Our sample allows us to analyze socio-demographic correlates of ambiguity attitudes and the updating of ambiguity attitudes to new information. Joint with Aljoscha Minnich and Hauke Roggenkamp.
Jan Obloj
Title: Optimal Transport perspective on robustness of stochastic optimization problems to model uncertainty
Abstract: We consider the sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We compare this with the more usual choice of balls in relative entropy/KL-divergence and argue Wasserstein balls are a better choice in most contexts. We provide explicit formulae for the first order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. The talk will focus on two simple examples: maximisation of expected utility and Black-Scholes call pricing. For the former, the results can be seen as giving the first order “Gilboa-Schmeidler correction to the classical EUM problem”. For the latter, they give a non-parametric version of Vega, one of the classical “Greeks”. The talk is based on joint works with Daniel Bartl, Samuel Drapeau, Yifan Jiang and Johannes Wiesel.
Luca Regis
Title: Coordinating dividend and capital regulation
Abstract: A risk-neutral manager runs a financial company generating stochastic cash flows facing time-varying macroeconomic conditions. The manager pays dividends to maximize shareholders' value without agency conflicts. Capital regulation requires holding reserves above a certain threshold, at which the manager can default or issue equity at a cost. Dividend regulation imposes taxes on payouts, depending on the state of the economy. We solve the firm's optimization problem and investigate how capital and dividend regulation affect its optimal policy. Counter-cyclical taxes on dividends reduce (foster) payouts and, thus, the firm's value in bad (good) times. At the same time, however, they reduce the maximal cost above which recapitalization is no longer ``incentive-compatible". Coordinating dividend taxes with counter-cyclical capital regulation can mitigate the latter effect, supporting the EU's COVID-19 policy of easing capital requirements while suspending bank dividends.
Maren Diane Schmeck
Title: From calendar time to business time: The case of commodity markets
Abstract: We address the problem of modelling commodity forward curves, while preserving empirical features observed in commodity markets. By letting a commodity market to "live" in the tempo of a business rather than calendar clock, we create a model with a rich but realistic set of features, such as stochastic volatility, stochastic rate of mean reversion and various shapes of forward curves such as backwardation and contango. The model, when applied to extensive historical datasets of crude oil and natural gas forward curves, shows a remarkably good fit to the observed futures prices, also in periods of high volatility and negative prices. The model is developed in such a way that it can be used for a wide variety of applications, ranging from exotic derivatives pricing to risk management of commodity portfolios.
H. Mete Soner
Title: McKean-Vlasov control and gradient flows.
Abstract: When one introduces interactions in a standard stochastic optimal control problem, the state dynamics are characterized by a McKean-Vlasov type stochastic differential equations and the natural state-space becomes the set of probability measures. In this talk, I outline the dynamic programming approach and the related partial differential equations on the Wasserstein spaces. In the so-called separable structure, the dynamics of the optimally controlled state process is of Langevin type. This connection, formally suggests a connection between the gradient flows and the control problems on the space of probability measures. I will illustrate this connection through the Kuramoto synchronization example. This talk is based on joint works with Rene Carmona, Quentin Cormier and Felix Hoefer.
Jacco Thijssen
Titel: First-best implementation in dynamic adverse selection models with news
Abstract: This paper shows that sale contracts with put options in favor of the buyer implement the full-information first-best allocation in a variety of dynamic adverse selection settings with news, which include the commonly-used arithmetic Brownian motion case. The implementation result holds regardless of whether news is public and verifiable (i.e., contractible) or privately observed by the buyer, and it does not require deep pockets on either side of the market. It is an implication of our implementation result that, irrespective of the assumptions on the game played, no agent waits for news to trade in such models.