Mathematical Finance Seminar – Fall 2018

Schedule for Fall 2018

Seminars are on Thursdays
Time: 4:10pm – 5:25pm
Location: Columbia University, 903 SSW (1255 Amsterdam Ave, between 121st and 122nd Street)

Organizers: Ruimeng Hu, Ioannis Karatzas, Marcel Nutz, Philip Protter

MAFN Seminar Archive


Julio Backhoff-Veraguas (Vienna)

Title: Model uncertainty in mathematical finance and the role of causal Wasserstein distances

Abstract: The problem of model uncertainty in financial mathematics has received considerable attention in the last years. This is particularly so for parametric models. In this talk I will follow a non-parametric point of view , focusing on the discrete-time case. I will argue that an insightful approach to model uncertainty should not be based on the familiar Wasserstein distances. I will then provide evidence supporting the better suitability of the recent notion of causal Wasserstein distances (also known as Nested Distances in the literature). Unlike their more familiar counterparts, these transport metrics take the role of information/filtrations explicitly into account. This talk is based on joint work with M. Beiglböck and D. Bartl.


Peter Carr (NYU)

Title: Valgebra

Arbitrage-free valuation of derivative securities is often an exercise in applied probability. However, when the underlying stochastic process is Markovian, it is well known that semi-groups arising in abstract algebra can be applied. We consider the possibility of using other algebraic structures for arbitrage-free valuation purposes.
We give an example  of arbitrage-free valuation which relies purely on deforming an algebraic structure. In our example, our purely algebraic approach leads to simpler valuation formulas than would arise by choosing simple stochastic processes. Joint work with Lin Yang.


Mark Podolskij (Aarhus)

Title: Statistical inference for fractional models

Abstract: In recent years, fractional and moving average type models have gained popularity in economics and finance. Most popular examples include fractional Brownian/stable motion, rough volatility models and Hawkes processes. In this talk we will review some existing estimation methods and present new theoretical results.


Johannes Muhle-Karbe (CMU) at 4:10 pm

TITLE: Liquidity in Competitive Dealer Markets

ABSTRACT: We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers’ demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an end-user market. This endogenously leads to a model with transient price impact. Smooth, diffusive, and discrete trades all incur finite but nontrivial liquidity costs, and can arise naturally from the liquidity takers’ optimization.
(Joint work with Peter Bank and Ibrahim Ekren)

Charles-Albert Lehalle (CFM) at 5:05 pm

Title: From optimal execution in front of a background noise to mean field games


A large number of mathematical frameworks are available to control optimally of the execution of a large order, and some frameworks are emerging to manage the life cycle of small orders in an orderbook. In all these framework an isolated investor faces a background noise coming from the aggregation of other market participants’ behaviors. With recent progresses in Mean Field Games (MFG), it is now possible to propose analyses of the same problems in a closed loop, going further than current isolated views. I will expose proposed approaches for both cases and explain how MFG can answer to a lot of needs in modeling liquidity on financial markets.


Luciano Campi (LSE)

Title: Mean-field games with absorption

Abstract: We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players’ states is described by a system of weakly interacting It{\^o} equations with absorption on first exit from a given set. Once a player exits, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean field game, the renormalization appears in form of a conditional law. We also consider the case of a system keeping track of the number of past absorbed players. Under fairly general assumptions, we show that in both cases a solution of the mean field game induces approximate Nash equilibria for the $N$-player games when $N$ is fairly large. This convergence is established provided the diffusion coefficient is non-degenerate. The degenerate case is more delicate and gives rise to counter-examples. The talk is based on joint works with Markus Fischer, Maddalena Ghio and Giulia Livieri.


Ruodu Wang (Waterloo)

“Robustness in the optimization of risk measures”

Over the past few years, there have been extensive debates on the comparative advantages of regulatory risk measures, Value-at-Risk (VaR) and Expected Shortfall (ES), in both academia and the banking and insurance industry. In particular, statistical robustness issues for these two risk measures have been a crucial consideration. In this talk, we focus on robustness in the optimization of risks. In contrast to the classic notion that VaR is statistically more robust than 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 notion of robustness is conceptually different from the field of robust optimization, to which some interesting links are discovered. This talk is based on joint work with Paul Embrechts and Alex Schied.


Scott Robertson (Boston University)

“Equilibria with Heterogeneous Information”
Abstract: We study equilibria in multi-asset and multi-agent continuous-time economies with asymmetric information and bounded rational noise traders. We establish existence of two equilibria. First, a full communication one where the informed agents’ signal is disclosed to the market, and static policies are optimal. Second, a partial communication one where the signal disclosed is affine in the informed and noise traders’ signals. Here, information asymmetry creates dynamic demands for portfolios which replicate linear and quadratic payoffs in the fundamental process. Results are valid for multiple dimensions; constant absolute risk averse investors; fundamental processes following a general diffusion; and non-linear terminal payoffs. Asset price dynamics and public information flows are endogenous, and are established using multiple filtration enlargements, in conjunction with predictable representation theorems for random analytic maps. Rational expectations equilibria are special cases of the general results. (Joint work with Jerome Detemple and Marcel Rindisbacher)

Ulrich Horst (HU Berlin)

Mean-Field Leader-Follower Games with Terminal State Constraint”

Abstract: We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a {convergence} result of the solutions with respect to certain perturbations of the drivers of both the forward and the backward component. The general results are used to solve a novel  single-player model of portfolio liquidation under market impact with expectations feedback as well as a novel Stackelberg game of optimal portfolio liquidation with asymmetrically informed players. The talk is based on Joint work with Guanxing Fu.

11/22/18 No seminar (Thanksgiving)

Yuchong Zhang (U Toronto)

“Large Tournament Games”

Abstract: We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank dependent, the equilibrium has a surprisingly explicit characterization, which allows us to conduct comparative statics and obtain explicit solution to several optimal reward design problems. In the general case when the players are heterogenous and payoffs are not purely rank dependent, we prove the existence, uniqueness and stability of the Nash equilibrium of the associated mean field game, and the existence of an approximate Nash equilibrium of the finite-player game. Our results have some potential economic implications; e.g., they lend support to government subsidies for R&D, assuming the profits to be made are substantial. (Joint work with Erhan Bayraktar and Jaksa Cvitanic)