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Mathias Beiglboeck

  1. Utility Maximization, Risk Aversion, and Stochastic Dominance.

    Ср, 04/06/2011 - 15:01 — SomNambul
    Authors: Mathias Beiglboeck, Johannes Muhle-Karbe, Johannes Temme
    Subjects: General Finance
    Abstract

    Consider an investor trading dynamically to maximize expected utility from
    terminal wealth. Our aim is to study the dependence between her risk aversion
    and the distribution of the optimal terminal payoff.

    Economic intuition suggests that high risk aversion leads to a rather
    concentrated distribution, whereas lower risk aversion results in a higher
    average payoff at the expense of a more widespread distribution.

  2. Is the minimum value of an option on variance generated by local volatility?.

    Пнд, 01/25/2010 - 16:01 — SomNambul
    Authors: Mathias Beiglboeck, Peter Friz, Stefan Sturm
    Subjects: Probability
    Abstract

    We discuss the possibility of obtaining model-free bounds on volatility
    derivatives, given present market data in the form of a calibrated local
    volatility model. A counter-example to a wide-spread conjecture is given.

  3. A General Duality Theorem for the Monge--Kantorovich Transport Problem.

    Втр, 11/24/2009 - 16:01 — SomNambul
    Authors: Mathias Beiglboeck, Christian Leonard, Walter Schachermayer
    Subjects: Optimization and Control
    Abstract

    The duality theory of the Monge--Kantorovich transport problem is analyzed in
    a general setting. The spaces $X, Y$ are assumed to be polish and equipped with
    Borel probability measures $\mu$ and $\nu$. The transport cost function
    $c:X\times Y \to [0,\infty]$ is assumed to be Borel. Our main result states
    that in this setting there is no duality gap, provided the optimal transport
    problem is formulated in a suitably relaxed way.

  4. On the Duality Theory for the Monge--Kantorovich Transport Problem.

    Втр, 11/24/2009 - 16:01 — SomNambul
    Authors: Mathias Beiglboeck, Christian Leonard, Walter Schachermayer
    Subjects: Optimization and Control
    Abstract

    The paper is accompanying "A general Duality Theorem for the
    Monge-Kantorovich Transport Problem". We explain the methods used in this
    article in an elementary setting and present two examples complementing the
    results obtained therein.

  5. An ultrafilter approach to Jin's Theorem.

    Пт, 08/21/2009 - 19:51 — SomNambul
    Authors: Mathias Beiglboeck
    Subjects: Combinatorics
    Abstract

    It is well known and not difficult to prove that if $C$ of integers has
    positive upper Banach density, the set of differences $C-C$ is syndetic, i.e.
    the length of gaps is uniformly bounded. More surprisingly, Renling Jin showed
    that whenever $A$ and $B$ have positive upper Banach density, then $A-B$ is
    piecewise syndetic.

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