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Jan Obloj

  1. Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model.

    Mon, 10/31/2011 - 15:01 — SomNambul
    Authors: Jan Obloj, Vladmir Cherny
    Subjects: Portfolio Management
    Abstract

    A drawdown constraint forces the current wealth to remain above a given
    function of its maximum to date. We consider the portfolio optimisation problem
    of maximising the long-term growth rate of the expected utility of wealth
    subject to a drawdown constraint, as in the original setup of Grossman and Zhou
    (1993). We work in an abstract semimartingale financial market model with a
    general class of utility functions and drawdown constraints. We solve the
    problem by showing that it is in fact equivalent to an unconstrained problem
    but for a modified utility function.

  2. Utility theory front to back - inferring utility from agents' choices.

    Thu, 01/20/2011 - 16:01 — SomNambul
    Authors: Jan Obloj, A.M.G. Cox, David Hobson
    Subjects: Portfolio Management
    Abstract

    We pursue an inverse approach to utility theory and consumption & investment
    problems. Instead of specifying an agent's utility function and deriving her
    actions, we assume we observe her actions (i.e. her consumption and investment
    strategies) and ask if it is possible to derive a utility function for which
    the observed behaviour is optimal. We work in continuous time both in a
    deterministic and stochastic setting. In a deterministic setup, we find that
    there are infinitely many utility functions generating a given consumption
    pattern.

  3. Arbitrage Bounds for Weighted Variance Swap Prices.

    Mon, 01/18/2010 - 16:01 — SomNambul
    Authors: Jan Obloj, Mark H.A. Davis, Vimal Raval
    Subjects: Pricing of Securities
    Abstract

    Consider a frictionless market trading a finite number of co-maturing
    European call and put options written on a risky asset plus an instrument with
    path-dependent payoff known as a weighted variance swap, e.g. a vanilla
    variance swap or a corridor variance swap. The question we ask is: Do the
    traded prices admit an arbitrage opportunity? We determine necessary and
    sufficient model-free conditions for the price of a continuously monitored
    weighted variance swap to be consistent with absence of arbitrage.

  4. On Azema-Yor processes, their optimal properties and the Bachelier-Drawdown equation.

    Mon, 08/31/2009 - 17:16 — SomNambul
    Authors: Laurent Carraro, Nicole El Karoui, Jan Obloj
    Subjects: Probability
    Abstract

    We study the class of Azema-Yor processes defined from a general
    semimartingale with a continuous running supremum process. We show that they
    arise as unique strong solutions of the Bachelier stochastic differential
    equation which we prove is equivalent to the Drawdown equation. Solutions of
    the latter have the drawdown property: they always stay above a given function
    of their past supremum. We then show that any process which satisfies the
    drawdown property is in fact an Azema-Yor process.

Math-arch

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