Post/Doctoral Seminar in Mathematical Finance

Modal title

Modal content

Autumn Semester 2015

Date / Time

Speaker

Title

Location

22 September 2015
15:15-16:15

Peter Bank
TU Berlin

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	Optimal investment with price impact
Speaker, Affiliation	Peter Bank, TU Berlin
Date, Time	22 September 2015, 15:15-16:15
Location	HG G 19.1
Abstract	We consider a financial model with price impact where an large investor’s orders affect bid and ask prices. In a Brownian setting with exponential utility, this model allows for an explicit description of optimal investment strategies. In order to learn about pricing and hedging risks in such a frictional model, we consider a quadratic benchmark problem which emerges heuristically as the high-resilience limit of the original one. The benchmark problem also allows for a closed-form solution. It turns out that, rather than trading towards the currently optimal position from a frictionless reference model, it is optimal to trade towards a weighted average of this positions future expected values. This is joint work in progress with Mete Soner and Moritz Voss.

Optimal investment with price impactread_more

HG G 19.1

29 September 2015
15:15-16:15

Sen Nevroz
McGill University, Montreal

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	Partially observed mean field games with a major player
Speaker, Affiliation	Sen Nevroz, McGill University, Montreal
Date, Time	29 September 2015, 15:15-16:15
Location	HG G 19.1
Abstract	In the Mean Field Games (MFG) framework where there is an agent (so-called Major) which has asymptotically non-vanishing influence on any other Minor agent, the best response control process of each Minor agent depends upon its own state, the Major agent's state and the conditional distribution of the generic minor agent, namely the system's stochastic mean field; this is in contrast to the basic MFG setup where the mean field is deterministic. The theory of MFG with a Major agent (MM-MFG) is well understood when the observations of the Minor agents are complete. In this talk we analyze the non-linear MM-MFG problem where each Minor agent partially observes the Major agent's state. We employ non-linear filtering theory derived for McKean-Vlasov type state equations and the Separation Principle in order to analyze the game in the infinite population limit. The main results are the existence and uniqueness of the solutions to the stochastic MFG system equations and the epsilon-Nash equilibrium property where the best response control process of each Minor agent depends upon the conditional density generated by that agent's non-linear filter together with the system's mean field and its own state. Work with Peter E. Caines.

Partially observed mean field games with a major playerread_more

HG G 19.1

* 13 October 2015
13:30-14:30

Matthias Lenga
University of Kiel

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	European representation of American options
Speaker, Affiliation	Matthias Lenga, University of Kiel
Date, Time	13 October 2015, 13:30-14:30
Location	ITS
Abstract	Given an American payoff g we ask the question if one can find an European claim that dominates g and such that the associated European value function coincides with g's value function within the continuation set. In a distributional sense, cheapest dominating European options seem to be natural candidates for the representing European claim. By the means on convex analysis, we provide within the Black Scholes setting a verification theorem for European representation.

European representation of American optionsread_more

ITS

20 October 2015
15:15-16:15

Matti Kiiski
ETH Zürich

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	Optional projection of a measurable integrand
Speaker, Affiliation	Matti Kiiski, ETH Zürich
Date, Time	20 October 2015, 15:15-16:15
Location	HG G 19.1
Abstract	We discuss the optional projection of a measurable integrand and its properties. Here, a measurable integrand means a time-dependent random field on the Euclidean space and the optional projection its time-dependent conditional expectation. We show that under suitable integrability conditions projection preserves lower semicontinuity and convexity. From applications perspective, these two properties are pretty much indispensable if one wants to guarantee the solvability of a minimization problem. If time permits, we discuss these minimization problems more in detail.

Optional projection of a measurable integrandread_more

HG G 19.1

3 November 2015
15:15-16:15

Anastasiia Zalashko
University of Vienna

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	Causal transport in discrete time and applications
Speaker, Affiliation	Anastasiia Zalashko, University of Vienna
Date, Time	3 November 2015, 15:15-16:15
Location	HG G 19.1
Abstract	In this talk we introduce a causal transportation problem. This is an optimal transport problem under additional linear constraints. Loosely speaking, causal transport plans are a relaxation of adapted processes in the same sense as Kantorovich transport plans are the extension of Monge-type transport maps. We establish a sound primal-dual picture of both causal and bicausal (causal in both directions) optimal transportation problems in discrete-time. Together with this, we provide a dynamic programming principle which allows us to show that Knothe-Rosenblatt rearrangement is often a bicausal optimal plan. Under the assumption of independent marginals of the source measure, we show that the optimal values of causal and bicausal transportation problems coincide. Finally, applications to some functional inequalities will be discussed.

Causal transport in discrete time and applicationsread_more

HG G 19.1

10 November 2015
15:15-16:15

Johannes Ruf

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	Some remarks on functionally generated portfolios
Speaker, Affiliation	Johannes Ruf,
Date, Time	10 November 2015, 15:15-16:15
Location	HG G 19.1
Abstract	In the first part of the talk I will review Bob Fernholz' theory of functionally generated portfolios. In the second part I will discuss questions related to the existence of short-term arbitrage opportunities. This is joint work with Ioannis Karatzas

Some remarks on functionally generated portfoliosread_more

HG G 19.1

17 November 2015
15:15-16:15

Matteo Burzoni
University of Milan

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	Arbitrage and hedging in robust models for finance
Speaker, Affiliation	Matteo Burzoni, University of Milan
Date, Time	17 November 2015, 15:15-16:15
Location	HG G 19.1
Abstract	We discuss fundamental questions of Mathematical Finance such as arbitrage and hedging in the context of a discrete time market with no reference probability. We show how different notions of arbitrage can be studied under the same general framework by specifying a class S of significant sets, and we investigate the richness of the family of martingale measures in relation to the choice of S. We also provide a superhedging duality theorem. We show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and observe how this is related to no-arbitrage considerations. We finally consider markets with frictions.

Arbitrage and hedging in robust models for financeread_more

HG G 19.1

24 November 2015
15:15-16:15

Zhenjie Ren
CMAP, Ecole Polytechnique

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	Path-dependent PDE: Theory and Applications
Speaker, Affiliation	Zhenjie Ren, CMAP, Ecole Polytechnique
Date, Time	24 November 2015, 15:15-16:15
Location	HG G 19.1
Abstract	Classical literature shows the relation between Markovian models and PDEs. Given the arising interest in the non-Markovian models in finance, we long to do analysis on path-dependent PDEs (PPDE). Ekren, Keller, Touzi and Zhang first introduced the notion of viscosity solutions to PPDEs. In this talk, we will review the recent development on this theory, in particular, some new arguments for the comparison results in both the semi-linear case and the fully-nonlinear case. Besides the theory, we will also show some applications of PPDEs.

Path-dependent PDE: Theory and Applicationsread_more

HG G 19.1

8 December 2015
15:15-16:15

Max Reppen
ETH Zürich

Event Details

Post/Doctoral Seminar in Mathematical Finance

Title	An optimal dividend problem
Speaker, Affiliation	Max Reppen, ETH Zürich
Date, Time	8 December 2015, 15:15-16:15
Location	HG G 19.1
Abstract	Optimizing dividends means finding the middle way between bankruptcy and owner profits, including the possibility of voluntary liquidation. In this talk we will briefly see one such problem with cash flows driven by an Ornstein-Uhlenbeck process. Proofs and technical results will be omitted from the presentation, in favor of studying the problem's more appreciable properties as well as trying to understand its obstacles.

An optimal dividend problemread_more

HG G 19.1

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location and if you want you can subscribe to the iCal/ics Calender.

Archive: AS 23 SS 23 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14