Mathematical Finance Seminar Series

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Schedule for Fall 2022

Seminars are on Thursdays
Time: 4:10pm - 5:25pm
Attention: All talks are available online, via Zoom. Select talks take place in hybrid mode. In-person participation is only available to Columbia affiliates with building access.

Join URL: https://columbiauniversity.zoom.us/j/98105307970?pwd=STFBanMvdmVLQ291Q1JwaVZFa3p1Zz09

Meeting ID: 946 7022 5225

Passcode: bachelier

Organizers: Gokce Dayanikli, Ioannis Karatzas, Marcel Nutz, Philip Protter, Johannes Wiesel

9/15/22

*This talk will take place online only.

Igor Cialenco (IIT)

Title: Risk Filtering and Risk-Averse Control of Systems with Model Uncertainty

Abstract: We consider a Markov decision process subject to model uncertainty in a Bayesian framework, where we assume that the state process is observed but its law is unknown to the observer. In addition, while the state process and the controls are observed at time t, the actual cost that may depend on the unknown parameter is not known at time t. The controller optimizes these running costs by using a family of special risk measures, that we call risk filters and that are appropriately defined to take into account the model uncertainty of the controlled system. These key features lead to non-standard and non-trivial risk-averse control problems, for which we derive the Bellman principle of optimality. We illustrate the general theory on several practically important examples.

9/23/22

This talk will take place online only.

 

Chao Zhou (NUS)

Special Date and Time: Friday 9/23/22 at 10:10am

Title: Large ranking games with diffusion control

Abstract: We consider a symmetric stochastic differential game where each player can control the diffusion intensity of an individual dynamic state process, and the players whose states at a deterministic finite time horizon are among the best of all states receive a fixed prize. Within the mean field limit version of the game we compute an explicit equilibrium, a threshold strategy that consists in choosing the maximal fluctuation intensity when the state is below a given threshold, and the minimal intensity otherwise. We show that for large n the symmetric n-tuple of the threshold strategy provides an approximate Nash equilibrium of the n-player game. We also derive the rate at which the approximate equilibrium reward and the best response reward converge to each other, as the number of players n tends to infinity. Finally, we compare the approximate equilibrium for large games with the equilibrium of the two-player case. This talk is based on the joint work with Stefan Ankirchner, Nabil Kazi-Tani and Julian Wendt.

9/29/22

This talk will take place online only.

Joseph Jackson (UT Austin)

Title: Well-posedness for non-Markovian quadratic BSDE systems with special structure.

Abstract: In this talk I will discuss some recent existence and uniqueness results for non-Markovian quadratic BSDE systems. Much of the talk will actually be about linear BSDEs, because it turns out that estimates for an appropriate class of linear BSDEs can be used to obtain existence results for quadratic systems. Indeed, the Malliavin derivative of a BSDE satisfies a linear BSDE, and strong enough estimates on the Malliavin derivative can be used to obtain existence. The difficulty in executing this strategy in the quadratic case is that the relevant linear BSDEs have unbounded coefficients, which a-priori can only be estimated in a space we call bmo. In a series of recent works with Gordan Žitković, I studied linear BSDEs with bmo coefficients systematically, and the following picture has emerged: both existence and uniqueness may fail for such equations, but can be recovered under various structural conditions.

 
 

10/6/22

*This talk will take place online only.

 

Thaleia Zariphopoulou (Austin)

Title: Mean-field games in Ito diffusion markets and general preferences

Abstract: I will introduce and discuss forward mean-field games of players with relative performance concerns in Ito diffusion markets. Under rather mild assumptions on their utilities and their types, I will present closed-form solutions for the value of the game, and the optimal processes. I will also discuss the case of partial information and derive solutions using an associated (ill-posed) Monge Ampere equation. 

 

 

10/20/22

 

 

10/27/22

*This talk will take place online only.

Ludovic Tangpi (Princeton)

Title: Optimal bubble riding in a large population

Abstract: Recent financial bubbles such as the emergence of cryptocurrencies and ``meme stocks" have attracted a large number of both retail and institutional investors. To study this phenomenon, we propose a game-theoretic model on optimal liquidation in the presence of an asset bubble. Our setup allows the influx of traders to fuel the price of the asset as they take advantage of the uptrend. However, traders face the risk of an inevitable (but unforeseen) market crash. In this talk we will argue that the above ``bubble riding game’’ gives rise to an interesting class mean field games. We will discuss solvability of the game and numerical simulations of the solution, which allow us to provide some intriguing insights on the relationship between the bubble burst and equilibrium strategies. This talk is based on a joint work with Shichun Wang (Princeton University).

11/3/22

*This talk will take place online only.

Wenpin Tang (Columbia IEOR)

Title: A prelude to blockchain technology: design and economy
 
Abstract: A blockchain is a distributed network which functions as a digit ledger and a smart contract allowing the secure transfer of assets without an intermediary. Bitcoin, a P2P electronic cash system, is the first manifestation of the blockchain technology. As the internet is a technology to facilitate the digit flow of information, the blockchain is a technology to facilitate the digital exchange of value. Due to its distributed and secure nature, blockchain technology is believed to be the next generation digital exchange platform with wide applications such as cryptocurrency, healthbank...etc. While the blockchain technology is conceptually powerful, it suffers from two major problems: scalability and security. In this talk, I will first give a "crash course" on the blockchain protocols, e.g. PoW (Proof of Work) and PoS (Proof of Stake). I will then focus on the PoS model, and show how this design may entail different types of  risks. I will also discuss a few challenges and research directions in the blockchain designs which are worth further developments. The work is based on joint work with David D. Yao.

11/10/22

 

Christoph Frei (Alberta)

Title: Principal Trading Arrangements: Optimality under Temporary and Permanent Price Impact

Abstract: We study the optimal execution problem in a principal-agent setting. A client (e.g., a pension fund, endowment, or other institution) contracts to purchase a large position from a dealer at a future point in time. In the interim, the dealer acquires the position from the market, choosing how to divide his trading across time. Price impact may have temporary and permanent components. There is hidden action in that the client cannot directly dictate the dealer's trades. Rather, she chooses a contract with the goal of minimizing her expected payment, given the price process and an understanding of the dealer's incentives. Many contracts used in practice prescribe a payment equal to some weighted average of the market prices within the execution window. We explicitly characterize the optimal such weights: they are symmetric and generally U-shaped over time. The talk is based on joint work with Markus Baldauf (University of British Columbia) and Joshua Mollner (Northwestern University).

11/17/22

Gudmund Pammer (ETH Zurich)

Title: The Wasserstein space of filtered processes

Abstract:
Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied mathematics. We believe that an appropriate probabilistic variant, the adapted Wasserstein distance (AW), can play a similar role for the class FP of filtered processes, i.e. stochastic processes together with a filtration. In contrast to other topologies for stochastic processes, probabilistic operations such as the Doob-decomposition, optimal stopping and stochastic control are
continuous w.r.t. AW. In this talk we will discuss recent developments of the Wasserstein space of filtered processes.

The talk is based on joint work with Daniel Bartl, Mathias Beiglböck, Stephan Eckstein, Stefan Schrott and Xin Zhang.

11/24/22

No Seminar (Thanksgiving)

12/1/22

 

Mathias Beiglböck (University of Vienna)

Title: The structure of martingale Benamou-Brenier in arbitrary dimensions

Abstract: In classical optimal transport, the contributions of Benamou–Brenier and McCann regarding the time-dependent version of the problem are
cornerstones of the field and form the basis for a variety of applications in other mathematical areas. Stretched Brownian motion provides an analogue for the martingale version of this problem. In
this article we provide a characterization in terms of gradients of convex functions, related to the characterization of optimizers in the classic transport problem for quadratic distance cost.

12/8/22

Walter Schachermayer (University of Vienna)

Title: A regularized Kellerer Theorem in arbitrary dimension

Abstract: We present a multidimensional extension of Kellerer's theorem on the existence of mimicking Markov martingales for peacocks, a term derived from the French for stochastic processes increasing in convex order. For a continuous-time peacock in arbitrary dimension, after Gaussian regularization, we show that there exists a strongly Markovian mimicking martingale It\^o diffusion. A novel compactness result for martingale diffusions is a key tool in our proof. Moreover, we provide counterexamples to show, in dimension $d \geq 2$, that uniqueness may not hold, and that some regularization is necessary to guarantee existence of a mimicking Markov martingale. Joint with G. Pammer (ETH Zürich), and B. Robinson (Univ. Vienna).

12/15/22

David Itkin (Imperial)

Title: Open Markets in Stochastic Portfolio Theory and Rank Jacobi Processes

Abstract: Stochastic portfolio theory is a framework to study large equity markets over long time horizons. In such settings investors are often confined to trading in an “open market” setup consisting of only assets with high capitalizations. In this work we relax previously studied notions of open markets and develop a tractable framework for them under mild structural conditions on the market.
Within this framework we also introduce a large parametric class of processes, which we call rank Jacobi processes. They produce a stable capital distribution curve consistent with empirical observations. Moreover, there are explicit expressions for the growth-optimal portfolio, and they are also shown to serve as worst-case models for a robust asymptotic growth problem under model ambiguity.
Lastly, the rank Jacobi models are shown to be stable with respect to the total number of stocks in the market. Time permitting, we will show that, under suitable assumptions on the parameters, the capital distribution curves converge to a limiting quantity as the size of the market tends to infinity. This convergence result provides a theoretical explanation for an important empirically observed phenomenon.
 

This talk is based on joint work with Martin Larsson.