Abstracts

John Birge

Title: Endogenous Connections and Risk Propagation in Financial Networks

Abstract: Connections among institutions in the global financial network create the potential for risk to propagate and for failures to cascade as successive institutions fail. Conditions, such as capital requirements, may change causing institutions to modify their behavior in ways that can fundamentally change the relationships among institutions and lead to substantially different failure dynamics. Increasing capital requirements can, for example, paradoxically increase the potential for failures to propagate by altering the intensity of relationships and risk exposures. Predicting such outcomes and directing policies to reduce overall systemic risk requires modeling of institutional responses to environmental conditions. This talk will discuss an approach based on inverse optimization of relationship decisions subject to capital constraints. A model of cascading failures and data from national debt cross-holdings illustrate the approach and demonstrate how changing capital requirements may lead to distinct differences in the sequences and extent of failures.

Peter Carr

Title: Adding Optionality

Abstract: Non-classical arithmetics replace ordinary addition and/or multiplication in standard arithmetic with other binary operations called pseudo-addition and multiplication. Dynamic non-classical arithmetic (DNA) allows a different non-classical arithmetic to be used at each time. We apply DNA to develop a novel arbitrage-free option pricing model in finance. Under our approach, European option valuation reduces to pseudo-addition of spot and strike, while Bermudan option valuation reduces to repeated pseudo-addition. Simple and realistic closed-form formulas are easily generated in both cases.

Hui Chen

Title: Predation or Self-Defense? Endogenous Competition and Financial Distress

Abstract: Firms tend to compete on prices more when they are in financial distress. More intense competition can in turn reduce firms' profit margins and push weaker firms further into distress. To study the quantitative effects of the feedback loop between industry competition and financial distress, we incorporate dynamic games of price competition into a model of long-term debt and strategic default. We show that this feedback mechanism endogenously generates stochastic volatility and jump risks in cash flows, and amplifies the risks of financial distress. Moreover, depending on the heterogeneity in customer bases and financial conditions across firms in an industry as well as across incumbent firms and new entrants, firms can exhibit a rich variety of strategic interactions, including predation, self-defense, and collaboration. Finally, we provide empirical support for our model's main predictions. This is joint work with Winston Dou, Hongye Guo, and Yan Ji.

Igor Cialenco

Title: Fair Capital Risk Allocation

Abstract: We propose a novel methodology for estimation of risk capital allocation, rooted in the theory of dynamic risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We introduce the concept of fair capital allocations and provide explicit formulae for fair capital allocations in case when the constituents of the risky portfolio are jointly normally distributed. The main focus of the paper is on the problem of approximating fair portfolio allocations in the case of not fully known laws of the portfolio constituents. We define and study the concepts of fair allocation estimators and asymptotically fair allocation estimators. We derive several estimators, and prove their fairness and/or asymptotic fairness under normality as well as in a nonparametric setup. Last, but not least, we propose two backtesting methodologies that are oriented at assessing the performance of the allocation estimation procedure. All concepts will be illustrated via a numerical study. This is joint work with Tomasz R. Bielecki (Illinois Tech), Marcin Pitera (Jagiellonian University) and Thorsten Schmidt (University of Freiburg)

Daniel Greenwald

Title: Financial Fragility with SAM

Abstract: Shared Appreciation Mortgages feature mortgage payments that adjust with house prices. They are designed to stave off borrower default by providing payment relief when house prices fall. Some argue that SAMs may help prevent the next foreclosure crisis. However, the home owner's gains from payment relief are the mortgage lender's losses. A general equilibrium model where financial intermediaries channel savings from saver to borrower households shows that indexation of mortgage payments to aggregate house prices increases financial fragility, reduces risk-sharing, and leads to expensive financial sector bailouts. In contrast, indexation to local house prices reduces financial fragility and improves risk-sharing.

Camilo Hernández

Title: A General Theory of Non-Markovian Consistent Planning

Abstract: In this work we develop a theory for continuous time non-Markovian stochastic control problems which are time-inconsistent. The distinguishing feature of these problems is that the classical Bellman optimality principle no longer holds. We adopt a sophisticated agent approach to study such problems meaning that we seek for consistent plans. Our problem is cast within the framework of a controlled non-Markovian forward SDE and a general objective functional setting. We introduce and motivate a new denition of equilibrium that incorporates a distinctive local feature which allows us to rigorously prove an extended DPP. Once a DPP is available, we can naturally associate a system of BSDEs, (H0), to this problem for which we are able to obtain a verification result. Moreover, such system is, at the same time, necessary to the study of this problem, i.e. given an equilibrium, its value function is naturally associated to a solution to (H0). In particular, we prove that an equilibrium must necessarily maximise the Hamiltonian of (P). Consequently, (H0) is fundamental to the study of time-inconsistent control problems for sophisticated agents. Finally, we provide a well{posedness result in the case the volatility of the state process is not controlled. Finally, a series of applications of the previous models are discussed.

Ruimeng Hu

Title: Deep Fictitious Play for Stochastic Differential Games

Abstract: We propose the deep fictitious play theory to compute the Nash equilibrium of asymmetric N-player non-zero-sum stochastic differential games. Specifically, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms, for which we refer as deep fictitious play, a multi-stage learning process. At each stage, we let individual player optimize her own payoff subject to the other playersí previous actions, equivalent to solve N decoupled stochastic control optimization problems, approximated by DNNs. Therefore, the fictitious play strategy leads to a structure consisting of N DNNs, which only communicate at the end of each stage. The resulted deep learning algorithm based on fictitious play is scalable, parallel and model-free, i.e., using GPU parallelization, it can be applied to any N-player stochastic differential game with different symmetries and heterogeneities (e.g., the existence of major players). We illustrate the performance of the deep learning algorithm by comparing to the closed-form solution of the linear-quadratic game. Moreover, we prove the convergence of fictitious play under appropriate assumptions and verify that the convergent limit forms an open-loop Nash equilibrium. We also extend the strategy of deep fictitious play to compute closed-loop Nash equilibrium for both homogeneous and inhomogeneous large N-player games.

Serdar Kadıoğlu

Title: Bayesian Deep Learning Based Exploration-Exploitation for Personalized Recommendations

Abstract: Personalized Recommendation Systems offer a fundamental capability to identify the most appropriate content at the best time for the right individual. At Fidelity Investments, we consider personalized engagement across multiple channels as a natural extension of our deep client relationship. From a practical perspective, applications of recommender systems require an effective technique to balance exploration and exploitation. For that purpose, in this talk we will present a novel approach based on Bayesian Deep Learning. For exploitation, we show how to capture rich contextual information, and for exploration, we demonstrate how to quantify uncertainty stemming from machine learning models as well as the underlying data.

Andreea Minca

Title: (In)Stability for the Blockchain: Deleveraging Spirals and Stablecoin Attacks

Abstract: We develop a model of stable assets, including noncustodial stablecoins backed by cryptocurrencies. Such stablecoins are popular methods for bootstrapping price stability within public blockchain settings. We demonstrate fundamental results about dynamics and liquidity in stablecoin markets, demonstrate that these markets face deleveraging spirals that cause illiquidity during crises, and show that these stablecoins have `stable' and `unstable' domains. Starting from documented market behaviors, we explain actual stablecoin movements; further our results are robust to a wide range of potential behaviors. In simulations, we show that these systems are susceptible to high tail volatility and failure. Our model builds foundations for stablecoin design. Based on our results, we suggest design features that can improve long-term stability and suggest methods for solving pricing problems that arise in existing stablecoins.

Oleksii Mostovyi

Title: Optimal Consumption from Investment and Labor Income in a Unifying Framework of Admissibility

Abstract: We consider a problem of optimal consumption from investment and labor income in an incomplete semimartingale market. We introduce a set of constraint times, i.e., a set of stopping times, at which the wealth process must stay positive, in a unifying way such that borrowing against the future income might be allowed or prohibited. Upon this, we increase dimensionality and treat as arguments of the value function not only the initial wealth but also a function that specifies the amount of labor income. Assuming finiteness of the primal and dual value functions and that the labor income is superreplicable (these are essentially the minimal model assumptions), we establish the existence and uniqueness of a solution to the underlying problem and provide several characterizations of the optimizer and the value functions. This talk is based on the joint work with Mihai Sirbu.

Dylan Possamaī

Title: Mean-Field Consumers for Electricity Demand-Response Programs.

Abstract: We study the problem of demand response contracts in electricity markets, considering a mean-field of consumers. We formulate the problem as a Principal-Agent problem with moral hazard in which the Principal is an electricity producer who observes continuously the consumption of a continuum of risk-averse consumers, and designs contracts in order to reduce her production costs. We prove that the producer can benefit from indexing contracts on the consumption of one Agent and aggregate consumption statistics from the distribution of the entire population of consumers. In the case of linear energy valuation, we provide closed-form solutions.

Kavita Ramanan

Title: Large deviations and concentration results for mean-field games

Abstract: Nash equilibria for multi-player games are notoriously hard to compute, even for moderate values of the number of players. In the case of suitably symmetric games, it has been shown over the last decade (under various sets of assumptions) that the Nash equilibria of n-player games converges to the solution of a corresponding limit game with a continuum of players, referred to as the mean-field game. We will describe concentration and large deviation results for the n-player Nash equilibria. This talk is based on joint work with F. Delarue and D. Lacker.

Alexander Schied

Title: Robustness in the optimization of risk measures

Abstract: We study issues of robustness of risk measures in the context of quantitative risk management. Depending on the underlying objectives, we develop a general methodology for determining whether a given risk measurement related optimization problem is robust. Motivated by practical issues from financial regulation, we give special attention to the two most widely used risk measures in the industry, Value-at-Risk (VaR) and Expected Shortfall (ES). We discover that for many simple representative optimization problems, VaR generally leads to non-robust optimizers whereas ES generally leads to robust ones. Our results thus shed light from a new angle on the ongoing discussion about the comparative advantages of VaR and ES in banking and insurance regulation. Our notion of robustness is conceptually different from the field of robust optimization, to which some interesting links are discovered. This is joint work with Paul Embrechts and Ruodu Wang.

Xiaofei Shi

Title: Liquidity Risk and Asset Prices

Abstract: We study how the price dynamics of an asset depends on its “liquidity” - the ease with which can be traded. An equilibrium is achieved through a system of coupled forward-backward SDEs, whose solution turns out to be amenable to an asymptotic analysis for the practically relevant regime of large liquidity. We also calibrate our model to time series data of market prices and trading volume, and discuss how to leverage deep-learning techniques to obtain numerical solutions. (Based on joint works in progress with Agostino Capponi, Lukas Gonon, Johannes Muhle-Karbe).

Mete Soner

Title: Optimal Dividends

Abstract: We consider the classical problem of optimal dividend policy of a firm. Following the traditional modeling we assume that the firm cash flow is a given stochastic process and dividends are paid from its cash holdings. Also bankruptcy occurs when these holdings are deleted. This model is widely used in the insurance and the corporate finance literature and is related to the real options. Although the dividends are paid discretely in a per-determined schedule, in the literature traditionally they are modeled as a continuous time process with no restrictions. In this talk, I discuss how to model the dividends in a period way and the impact of this restriction on the optimal policies.

Ludovic Tangpi

Title: On Backward Propagation of Chaos

Abstract: In this talk we will present a generalization of the theory of propagation of chaos to backward (weakly) interacting diffusion. The focus will be on cases allowing for explicit convergence rates and concentration inequalities for the empirical measures. Among other consequences, we derive the approximation of some non-local, second order PDEs on an infinite dimensional space by a sequence of parabolic PDEs on finite dimensional spaces. The talk is based on join works with M. Lauriere.

Tim-Kam Leonard Wong

Title: Universal portfolio and stochastic portfolio theory

Abstract: In his seminal paper Cover constructed what is now called an online investment algorithm by forming a Bayesian average over the constant-weighted portfolios, and showed that its growth rate is asymptotically optimal in the given class. We extend this result to the setting of stochastic portfolio theory where the portfolios are functions of the market weights. In the second part of the talk we consider the problem of constructing suitable prior distributions on the infinite dimensional space of portfolio generating functions. Mathematically, this corresponds to novel probability measures on a space of concave functions. Based on joint works with Walter Schachermayer, Christa Cuchiero and Peter Baxendale.

Jiacheng Zhang

Title : Inverting the Markovian Projection, with an Application to Local Stochastic Volatility Models

Abstract : We study two-dimensional stochastic differential equations (SDEs) of McKean--Vlasov type in which the conditional distribution of the second component of the solution given the first enters the equation for the first component of the solution. Such SDEs arise when one tries to invert the Markovian projection developed by Gyongy (1986), typically to produce an ItÙ process with the fixed-time marginal distributions of a given one-dimensional diffusion but richer dynamical features. We prove the strong existence of stationary solutions for these SDEs, as well as their strong uniqueness in an important special case. Variants of the SDEs discussed in this paper enjoy frequent application in the calibration of local stochastic volatility models in finance, despite the very limited theoretical understanding.

Limin Zhang

Title: Machine Learning in Mortgages

Abstract: We discuss an application of machine learning to the valuation of mortgage backed securities (MBS). This requires projecting the behavior of the borrowers over the next 5 to 10 years along various macro scenarios. We do have a large amount of clean data, but the long run projections, in macro scenarios that have often not been seen in the past, prove especially challenging for the technique. We show how expert-driven feature engineering can dramatically improve the predictive ability of the model. We have implemented and use the model for actual mortgage valuation and show how the results can improve upon existing methodologies.

Xin Zhang

Title: Transport Plans with Domain Constraints

Abstract: Let $\Omega$ be one of $\mathbb{X}^{N+1},C[0,1],D[0,1]$: product of Polish spaces, space of continuous functions from $[0,1]$ to $\mathbb{R}^d$, and space of RCLL (right-continuous with left limits) functions from $[0,1]$ to $\mathbb{R}^d$, respectively. We first consider the existence of a probability measure $P$ on $\Omega$ such that $P$ has the given marginals $\alpha$ and $\beta$ and its disintegration $P_x$ must be in some fixed $\Gamma(x) \subset \mathfrak{P}(\Omega)$, where $\mathfrak{P}(\Omega)$ is the set of probability measures on $\Omega$. The main application we have in mind is the martingale optimal transport problem when the martingales are assumed to have bounded volatility/quadratic variation.

We show that such probability measure exists if and only if the $\alpha$ average of the so-called $G$-expectation of bounded continuous functions with respect to the measures in $\Gamma$ is less than their $\beta$ average.

As a byproduct, we get a necessary and sufficient condition for the Skorokhod embedding for bounded stopping times. Second, we consider the optimal transport problem with constraints and obtain the Kantorovich duality. A corollary of this result is a monotonicity principle which gives us a geometric way of identifying the optimizer.