Post/Doctoral Seminar in Mathematical Finance

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Spring Semester 2016

Date / Time

Speaker

Title

Location

2 February 2016
15:15-16:15

Aditi Dandapani
Columbia University

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Post/Doctoral Seminar in Mathematical Finance

Title	Strict local martingales via filtration enlargement
Speaker, Affiliation	Aditi Dandapani, Columbia University
Date, Time	2 February 2016, 15:15-16:15
Location	HG G 19.1
Abstract	Strict local martingale arise naturally in applications, most notably in the modeling of financial bubbles. Beginning with a non negative model following a stochastic differential equation with stochastic volatility, we show how a strict local martingale might arise from a true martingale as a result of an enlargement of the underlying filtration. More precisely, we implement a particular type of enlargement, an "initial expansion" of the filtration, for various kinds of stochastic differential equation models, and we provide sufficient conditions such that this expansion can turn a martingale into a strict local martingale. Applications of our work include the modeling and detection of financial bubbles. For example, one might postulate that a bubble arises as a result of the arrival of new information, which we can model via an enlargement of the filtration.

Strict local martingales via filtration enlargementread_more

HG G 19.1

23 February 2016
15:15-16:15

Ying Hu
Université de Rennes 1

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Post/Doctoral Seminar in Mathematical Finance

Title	An ergodic BSDE approach to large time behaviour of solution of semilinear parabolic partial differential equation
Speaker, Affiliation	Ying Hu, Université de Rennes 1
Date, Time	23 February 2016, 15:15-16:15
Location	HG G 19.1
Abstract	This talk is devoted to the study of the large time behaviour of solution of some semilinear parabolic partial differential equation (with Dirichlet or Neumann boundary condition). A probabilistic method (more precisely, an approach via an ergodic backward stochastic equation) is developped to show that the solution of a parabolic semilinear PDE at large time $T$ behaves like a linear term $\lambda T$ shifted with a function $v$, where $(v,\lambda)$ is the solution of the ergodic PDE associated to the parabolic PDE. The advantage of our method is that it gives an explicit rate of convergence. The result gives a perspective to give a precise estimate on the long run asymptotics for utility maximisation.

An ergodic BSDE approach to large time behaviour of solution of semilinear parabolic partial differential equationread_more

HG G 19.1

22 March 2016
15:15-16:30

Danijel Zivoi
ETH Zurich, Switzerland

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Post/Doctoral Seminar in Mathematical Finance

Title	Mean-variance with deterministic information
Speaker, Affiliation	Danijel Zivoi, ETH Zurich, Switzerland
Date, Time	22 March 2016, 15:15-16:30
Location	HG G 19.1
Abstract	In a market model where the trader is allowed to use only deterministic strategies for trading in the risky asset, we analyze the problems of mean-variance hedging and mean-variance portfolio optimization. We work with a class of models for stock price processes that are given by S_t = S₀ + f(t) + g(t)Y_t* for deterministic functions f and g and a square-integrable martingale Y. This class is flexible enough to include arithmetic and exponential Lévy models. We present explicit solutions of trading strategies in terms of the model parameters (S₀, f, g, Y) and of the Galtchouk–Kunita–Watanabe decomposition of the contingent claim H. Surprisingly, the main tool for the analysis is the integration by parts formula for functions of finite variation.

Mean-variance with deterministic informationread_more

HG G 19.1

5 April 2016
15:15-16:30

Daniel Balint
ETH Zurich, Switzerland

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Post/Doctoral Seminar in Mathematical Finance

Title	Financial bubbles in a numéraire-independent framework with infinite continuous time
Speaker, Affiliation	Daniel Balint, ETH Zurich, Switzerland
Date, Time	5 April 2016, 15:15-16:30
Location	HG G 19.1
Abstract	Our aim is to generalize the numéraire-independent approach of Herdegen and Schweizer ('15) for defining and analyzing financial bubbles from finite to infinite time horizon. In the above paper the concepts of bubbly markets rely heavily on the notion of maximal strategies, which requires a final payoff in the standard finite time horizon framework. In the infinite time horizon case, we introduce several alternative approaches to describe maximality and investigate their reasonability. We motivate appropriate choice of maximality notion by establishing connections to NUPBR in the sense of Delbaen and Schachermayer ('94). After this preparation, we are able to recover dual characterization of bubbly markets in infinite time horizon involving numéraires and martingale measures and show that a market is bubbly if and only if all possible valuation measures for all possible discounted asset prices always lead to local martingales which are not uniformly integrable (they might be true martingales though). This, in particular, represents an improvement of the bubble characterization given by Protter ('13).

Financial bubbles in a numéraire-independent framework with infinite continuous timeread_more

HG G 19.1

12 April 2016
15:15-16:30

Dr. Anne MacKay
ETH Zurich, Switzerland

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Post/Doctoral Seminar in Mathematical Finance

Title	Can quantile hedging explain funding practices for pension plans?
Speaker, Affiliation	Dr. Anne MacKay, ETH Zurich, Switzerland
Date, Time	12 April 2016, 15:15-16:30
Location	HG G 19.1
Abstract	In a complete bond market, payoffs that depend on the term structure of interest rates can be perfectly replicated by a hedging strategy whose initial cost is the risk-neutral price of the payoff. Quantile hedging may reduce the cost of the strategy if the investor is willing to accept the risk that, with low probability, the payoff will not be perfectly replicated. In this paper, we use the results from Föllmer & Leukert (1999) to assess whether the cost of a quantile hedging strategy can be reduced by the introduction of a risky asset in the complete bond market. In a simplified market model, we derive explicit expressions for the initial cost of the hedge and the expectation of the unhedged loss. We show that while investing in the risky asset can reduce the cost of the hedge, it also increases the expectation of the loss. These results are presented with applications to pension plan funding in mind.

Can quantile hedging explain funding practices for pension plans?read_more

HG G 19.1

19 April 2016
15:15-16:30

Thomas Cayé
ETH Zurich, Switzerland

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Post/Doctoral Seminar in Mathematical Finance

Title	Nonlinear transaction costs, portfolio choice, and time-varying investment opportunities
Speaker, Affiliation	Thomas Cayé, ETH Zurich, Switzerland
Date, Time	19 April 2016, 15:15-16:30
Location	HG G 19.1
Abstract	We consider a market with one safe asset and one risky asset with general, not necessarily Markovian dynamics. In this setting, we study the tradeoff between expected returns, the variance of the corresponding positions, and nonlinear trading costs proportional to a power of the order flow. In the limit for small costs, the optimal strategy is given by the renormalized solution of an ordinary differential equation. We show as well that to the first order this problem is equivalent to maximizing the expected utility of an investor with constant absolute risk aversion.

Nonlinear transaction costs, portfolio choice, and time-varying investment opportunitiesread_more

HG G 19.1

26 April 2016
15:15-16:30

Dr. Ibrahim Ekren
ETH Zurich, Switzerland

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Post/Doctoral Seminar in Mathematical Finance

Title	Hormander condition for delay equations
Speaker, Affiliation	Dr. Ibrahim Ekren, ETH Zurich, Switzerland
Date, Time	26 April 2016, 15:15-16:30
Location	HG G 19.1
Abstract	In this talk we will present some partial results that improve the Hormander condition for delay equations. We will state a condition that takes into account and quantifies the noise introduced to the system through the delay. This is based on joint work with Reda Chhaibi which is still in progress.

Hormander condition for delay equationsread_more

HG G 19.1

* 3 May 2016
15:15-16:30

Lukas Gonon
ETH Zurich, Switzerland

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Post/Doctoral Seminar in Mathematical Finance

Title	Continuous-time martingale transport with jumps: explicit examples
Speaker, Affiliation	Lukas Gonon, ETH Zurich, Switzerland
Date, Time	3 May 2016, 15:15-16:30
Location	HG F 26.5
Abstract	Motivated by robust finance, martingales that have a given family of probability measures as their one-dimensional marginal distributions have been extensively studied. In order to build and study toy models, it is desirable to have explicit examples of continuous-time martingales with prescribed marginal laws at initial and terminal time available. While there exists a variety of such processes with continuous trajectories, examples with jumps are scarce. In this talk we use time-changed Lévy processes to construct a class of such examples.

Continuous-time martingale transport with jumps: explicit examplesread_more

HG F 26.5

10 May 2016
15:15-16:30

Mark-Roman Feodoria
Christian-Albrechts-Universität zu Kiel

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Post/Doctoral Seminar in Mathematical Finance

Title	Portfolio optimization under fixed transaction costs
Speaker, Affiliation	Mark-Roman Feodoria, Christian-Albrechts-Universität zu Kiel
Date, Time	10 May 2016, 15:15-16:30
Location	HG G 19.1
Abstract	We consider an investor with constant absolute risk aversion trading in a market consisting of one safe and one risky asset with general Itō dynamics. We assume that she has to pay a fixed transaction cost ε for each trade regardless of its size. Using a non-Markovian dynamic programming approach we derive the leading order optimal trading strategy and state rigorous verification theorems. We give examples and present an application to utility indifference pricing. Our results verify the heuristics of [2, Section 5] in the absence of proportional costs, but for general Itō dynamics. Contrary to the related study of [1] in a different setup our derivation and verification rely on martingale methods and tools from stochastic calculus like [3] rather than homogenization and viscosity solutions. This is a joint work with Jan Kallsen. References [1] Albert Altarovici, Johannes Muhle-Karbe, and Halil Mete Soner. Asymptotics for fixed transaction costs. Finance and Stochastics, 19(2):363‒414, 2015. [2] Ralf Korn. Portfolio optimisation with strictly positive transaction costs and impulse control. Finance and Stochastics, 2(2):85‒114, 1998. [3] Goran Peskir. A change-of-variable formula with local time on curves. Journal of Theoretical Probability, 18(3):499‒535, 2005.

Portfolio optimization under fixed transaction costsread_more

HG G 19.1

17 May 2016
15:15-16:30

Prof. Dr. Christoph Czichowsky
London School of Economics

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Post/Doctoral Seminar in Mathematical Finance

Title	The risk tolerance process and the sensitivity of optimal investment and consumption
Speaker, Affiliation	Prof. Dr. Christoph Czichowsky, London School of Economics
Date, Time	17 May 2016, 15:15-16:30
Location	HG G 19.1
Abstract	In this talk, we investigate the sensitivity of optimal trading strategies and consumption streams with respect to the current level of wealth. It turns out that both sensitivities can be expressed via the so-called risk tolerance process. They appear quite naturally in various expansions of portfolio optimisation problems. Existence and several dynamic characterisations are established in a general semimartingale setting, building on earlier results of Kramkov and Sirbu (2006, 2007). The talk is based on joint work with Jan Kallsen and Johannes Muhle-Karbe.

The risk tolerance process and the sensitivity of optimal investment and consumptionread_more

HG G 19.1

31 May 2016
15:15-16:30

Dr. Martin Herdegen
ETH Zurich, Switzerland

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Post/Doctoral Seminar in Mathematical Finance

Title	On the dual characterisation of NA and NA₊
Speaker, Affiliation	Dr. Martin Herdegen, ETH Zurich, Switzerland
Date, Time	31 May 2016, 15:15-16:30
Location	HG G 19.1
Abstract	The dual characterisation of no-arbitrage conditions is a classic problem in Mathematical Finance. In this talk, we focus on the condition NA. For continuous semimartingales, a dual characterisation in terms of absolutely continuous local martingale measures (ACLMMs) has been obtained by Strasser (2005) and Kabanov/Stricker (2005) building on earlier work by Delbaen/Schachermayer (1995) and Levental/Skorohod (1995). For general semimartingales, the result by Delbaen/Schachermayer has been extended in the PhD thesis of Brannath (1997), proving the existence of an ACLMM under an additional condition which cannot be dropped in general. In this talk, we establish a kind of converse to the result of Brannath by presenting a sufficient dual condition for NA in the spirit of Strasser and Kabanov/Stricker for general semimartingales. Our result also allows to give a sufficient dual condition for the weaker condition NA₊, which has also been studied by Strasser. This is joint work in progress with Sebastian Herrmann.

On the dual characterisation of NA and NA₊read_more

HG G 19.1

21 June 2016
15:15-16:30

Prof. Dr. Kasper Larsen
Carnegie Mellon University

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Post/Doctoral Seminar in Mathematical Finance

Title	Radner equilibrium in incomplete Lévy models
Speaker, Affiliation	Prof. Dr. Kasper Larsen, Carnegie Mellon University
Date, Time	21 June 2016, 15:15-16:30
Location	HG G 19.1
Abstract	We construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors’ income rates as well as the stock’s dividend rate are governed by discontinuous Lévy processes. Our main result provides the equilibrium (i.e., bond and stock price dynamics) in closed-form. As an application, we show that the equilibrium Sharpe ratio can be increased and the equilibrium interest rate can be decreased (simultaneously) when the investors’ income streams cannot be traded. Joint work with T. Sae-Sue.

Radner equilibrium in incomplete Lévy modelsread_more

HG G 19.1

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