Mathematical Finance Seminar – Spring 2016

probfinmathSchedule for Spring 2016

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

Organizers: Ioannis Karatzas, Philip Protter, Marcel Nutz, Yuchong Zhang




Yuchong Zhang (Columbia)

Title: Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty


We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly non-dominated. Using a backward-forward scheme, we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that when the market consists of multiple dynamically traded assets and satisfies efficient friction, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of strictly consistent price systems. (Joint work with Erhan Bayraktar)


Dylan Possamai (Paris Dauphine)

Title:Dynamic Programming Approach to Principal-Agent Problems


We consider a general formulation of the Principal-Agent problem from Contract Theory, on a finite horizon. We show how to reduce the problem to a stochastic control problem which may be analyzed by the standard tools of control theory. In particular, Agent’s value function appears naturally as a controlled state variable for the Principal’s problem. Our argument relies on the Backward Stochastic Differential Equations approach to non-Markovian stochastic control, and more specifically, on the most recent extensions to the second order case. This is a joint work with Jaksa Cvitanic and Nizar Touzi.


Christina Dan Wang (Columbia University)

“The observed standard error of high-frequency estimators for parameters containing jumps”


In high frequency inference, standard errors are important: they are used both to assess the precision of estimators and also when building forecasting models. Due to the scarcity of methodology to assess this uncertainty – standard error, this paper provides an alternative solution to this problem. It provides a general nonparametric method for assessing asymptotic variance (AVAR) and consistent estimators of AVAR for a class of integrated parameters. The parameter process can be a general semi-martingale with both continuous and jump components. The integrand of the integrated parameter can also contain jump components. The methodology applies to a wide variety of estimators, such as integrated volatility and leverage effect.


Umut Cetin (LSE)


Andrew Lesniewski (Baruch) – CANCELLED


Daniel Lacker (Brown)

“Liquidity, risk measures, and concentration of measure”


Expanding on techniques of concentration of measure, we propose a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(\rho(\lambda X))_{\lambda \ge 0}$, where $\rho$ is a convex risk measure and $X$ a financial position (a random variable), and we call such a curve a “liquidity risk profile.” For some notable classes of risk measures, especially shortfall risk measures, the shape of a liquidity risk profile is intimately linked with the tail behavior of the underlying $X$. We exploit this link to systematically bound liquidity risk profiles from above by other real functions $\gamma$, deriving tractable necessary and sufficient conditions for concentration inequalities of the form $\rho(\lambda X) \le \gamma(\lambda)$ for all $\lambda \ge 0$. These concentration inequalities admit useful dual representations related to transport-entropy inequalities, and this leads to efficient uniform bounds for liquidity risk profiles for large classes of $X$. An interesting question of tensorization of concentration inequalities arises when we seek to bound the liquidity risk profile of a combination $f(X,Y)$ of two positions $X$ and $Y$ in terms of their individual liquidity risk profiles. Specializing to law invariant risk measures, we uncover a surprising connection between tensorization and certain time consistency properties known as acceptance and rejection consistency, which leads to some new mathematical results on large deviations and dimension-free concentration of measure.


Alexander Schnurr (Siegen)

“An Efficient Way to Analyze Path and Distributional Properties of Processes Used In Mathematical Finance.”

In the theory of Levy processes, the characteristic exponent and the Blumenthal-Getoor index are two of the main tools in order to describe and to analyze properties of the process. These concepts have been used for over the past fifty years. In our talk we show how these concepts were generalized recently to the class of homogeneous diffusions with jumps. This class of processes contains the solutions of Levy driven SDEs, certain Feller processes and various classes which are used in mathematical finance. At the end of the talk we present five different applications.


No seminar (spring recess)


No seminar (Berkeley-Columbia meeting)


Nicholas Westray (Citadel)

“Optimal Execution for Orders with a Market on Close Benchmark in Hong Kong”

The closing benchmark in Hong Kong, the median of 5 nominal prices over the last trading minute, has attracted a lot of attention recently, both positive and negative.

In this talk we give an overview of closing auctions globally and discuss the situation in Hong Kong in detail. We suggest a model for the closing auction period which captures the key microstructure features and allows us to derive an optimal strategy for a trader seeking to benchmark themselves against the closing price. We evaluate the theoretical results against real data for the Hang Seng and discuss the conclusions.

This is joint work with Christoph Frei (University of Alberta).


Ronnie Sircar (Princeton)

“Fracking, Renewables & Mean Field Games”

The dramatic decline in oil prices, from around $110 per barrel in June 2014 to around $30 in January 2016 highlights the importance of competition between different energy sources.  Indeed, the price drop has been primarily attributed to OPEC’s strategic decision not to curb its oil production in the face of increased supply of shale gas and oil in the US.  We study how continuous time Cournot competitions, in which firms producing similar goods compete with one another by setting quantities, can be analyzed as continuum dynamic mean field games.  We illustrate how the traditional oil producers may react in counter-intuitive ways in face of competition from alternative energy sources.


Martin Larsson (ETH Zurich)

Title: Polynomial diffusions on the unit ball

Abstract: Polynomial processes are defined by the property that conditional expectations of polynomial functions of the process are again polynomials of the same or lower degree. Many fundamental stochastic processes are polynomial, and their tractable structure makes them important in applications. For instance, every affine process is polynomial. In this talk I will review these notions, and then focus on polynomial diffusions whose state space is the unit ball. This naturally leads to the classical algebraic problem of representing nonnegative polynomials as sums of squares, where I will present new results as well as an open problem. The sum-of-squares property, in turn, is connected to probabilistic properties of the original process, such as pathwise uniqueness and existence of smooth densities.


(Cancelled) – Alfred Galichon (NYU and Sciences Po)


Ashkan Nikeghbali (University of Zurich)

“Graphical methods to model dependence and limit theorems”

In this talk, I will consider the simple example of sums of bounded random variables, which typically occurs in the modelling of credit loss portfolios, and give a few conditions on the dependency graphs under which one can prove limit theorems and estimate the tails of the distributions.