Seminar on Mathematical Finance - summer term 2013

Time: Thursday, 17:00-18:30
Room: Seminarraum Olga Taussky-Todd C 2.09, UZA4, Nordbergstraße 15, 2.OG
Organizer: Walter Schachermayer
Topic: Model-free valuation of financial derivatives

Date:	Speaker:	Title :
Mo, 25/02/13 17:00-18:30 Different time!	Yan Dolinsky	Robust Hedging with Proportional Transaction Costs
	Abstract: Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at maturity. Only stock trading is subject to proportional transaction costs. The main theorem is duality between hedging and a Monge-Kantorovich type optimization problem. In this dual transport problem the optimization is over all the probability measures which satisfy an approximate martingale condition related to consistent price systems in addition to the usual marginal constraints.

Thu, 07/03/13 17:00-18:30	Nizar Touzi	An Explicit Martingale Version of Brenier's Theorem (Joint work with Pierre Henry-Labordere)
	Abstract: The martingale optimal transportation problem is motivated by model-independent bounds for exotic options in financial mathematics. In this paper, we extend the one-dimensional Brenier's theorem to the present martingale version. We provide the explicit martingale optimal transference plans for a remarkable class of coupling functions corresponding to the lower and upper bounds. These explicit extremal probability measures coincide with the unique left and right monotone martingale transference plans, introduced by M. Beiblbock and N. Juillet, who established existence and uniqueness by suitable adaptation of the notion of cyclic monotonicity. Instead, our approach relies heavily on the (weak) duality result, and provides, as a by-product, an explicit expression for the corresponding optimal semi-static hedging strategies. We finally provide an extension to the multiple marginals case. The continuous-time limit provides a remarkable PCOC process, namely a pure jump martingale local Levy process with prescribed marginals.

Thu, 14/03/13 17:00-18:30	Marcel Nutz	Arbitrage and Duality in Nondominated Discrete-Time Models
	Abstract: We study a nondominated model of a discrete-time financial market where stocks are traded dynamically and options are available for static hedging. In a general measure-theoretic setup, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a family of martingale measures with certain properties. In the arbitrage-free case, we show that optimal superhedging strategies exist for general contingent claims, and that the minimal superhedging price is given by the supremum over the martingale measures. (Joint work with Bruno Bouchard.)

Thu, 21/03/13 17:00-18:30	Pietro Siorpaes	Uniform integrability with respect to a semimartingale
	Abstract: We introduce the notion of uniform integrability with respect to a semimartingale, and we derive theorems for stochastic integrals analogous to the classical ones for Lebesgue Integrals and uniform integrability with respect to a measure. In particular, we generalize the stochastic dominated convergence theorem -obtaining a condition which is both necessary and sufficient for the convergence of stochastic integrals- and we provide multiple criteria that allow to show uniform integrability of a given sequence of integrands.

Thu, 11/04/13 17:00-18:30	Florian Stebegg	The asymptotic theory of transaction costs: Models on finite probability spaces
	Student presentation.

Thu, 18/04/13 17:00-18:30	No Seminar	Please notice the Conference on Current Topics in Mathematical Finance

Thu, 25/04/13 17:00-18:30	Elisabeth Prossinger	Utility maximization under transaction costs: The case of finite probability spaces
	Student presentation.

Thu, 02/05/13 17:00-18:30	Luis G. Gorostiza	Oscillatory Fractional Brownian Motion and Related Processes
	Abstract: PDF

Thu, 16/05/13 17:00-18:30	Yiqing Lin	A new result for second order BSDEs with quadratic growth and its applications
	Abstract: In this talk, we introduce a class of second order backward stochastic differential equations (2BSDEs) with quadratic growth in coefficients. The solvability for such 2BSDEs and applications to robust utility maximization problems are presented.

Thu, 23/05/13 17:00-18:30	Ivar Ekeland	A simple model of a commodity market.
	Abstract: In commodities markets, physical markets (where the commodity itself is traded) coexist with financial markets (where future contracts are traded). The primary use of futures is to enable commodity traders to hedge their risks. However, financial markets are open as well to money managers, who are not interested in the commodity itself, but in the risk. The influence they have on prices has been much debated. We give a simple model, perhaps the simplest possible, of a commodity market where a physical market coexists with a financial market, and we analyse the influence of speculators on the average level and volatility of prices. This is joint work with Delphine Lautier and Bertrand Villeneuve. The paper can be found here

Thu, 06/06/13 17:00-18:30	No Seminar	No Seminar

Thu, 13/06/13 17:00-18:30	Fabian Pühringer	General duality theory: The continuous case I
	Student presentation.

Thu, 20/06/13 17:00-18:30	Magdalena Mujetic	General duality theory: The continuous case II
	Student presentation.

Mon, 01/07/13 11:30-12:30 Room D 107 Different time and place!	Christian Bender	A first-order BSPDE for swing option pricing
	Abstract: In a swing option contract, the holder of the option can buy some volume of a commodity, say electricity, for a fixed strike price during the lifetime of the option. There are typically local constraints on how much volume can be exercised at a given time, and global constraints on the total volume. We consider the pricing problem of a stylized version of a swing option contract as an optimal control problem in a general non-Markovian setting in continuous time, and show that the value process of this control problem solves a non-linear first-order backward stochastic differential equation. Based on this result we can characterize the set of optimal controls and derive a dual minimization problem. We also discuss smoothness of the value process under the assumption that the payoff process of the swing option is leftcontinuous in expectation. It turns out that, under this additional assumption, the value process is the unique 'classical' (in an appropriate sense) solution to the BSPDE. This talk is based on joint work with Nikolai Dokuchaev (Curtin University).