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Yu-Jui Huang

  1. Robust Maximization of Asymptotic Growth under Covariance Uncertainty.

    Mon, 07/18/2011 - 15:01 — SomNambul
    Authors: Erhan Bayraktar, Yu-Jui Huang
    Subjects: Portfolio Management
    Abstract

    This paper resolves a question proposed in Kardaras and Robertson (2011): how
    to invest in a robust growth-optimal way in a market where precise knowledge of
    the covariance structure of the underlying process is unavailable. Among an
    appropriate class of admissible covariance structures, we characterize the
    optimal trading strategy in terms of a generalized version of a principal
    half-eigenvalue of a Pucci extremal operator and its associated eigenfunction.

  2. On the Multi-Dimensional Controller and Stopper Games.

    Tue, 09/07/2010 - 15:02 — SomNambul
    Authors: Erhan Bayraktar, Yu-Jui Huang
    Subjects: Optimization and Control
    Abstract

    We consider a zero-sum stochastic differential controller-and-stopper game in
    which the state process is a controlled jump-diffusion evolving in a
    multi-dimensional Euclidean space. In this game, the controller affects both
    the drift and the volatility terms of the state process. Under appropriate
    conditions, we show that the lower value function of this game is a viscosity
    solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation, by
    generalizing the weak dynamic programming principles in [3].

  3. Outperforming the Market Portfolio with a Given Probability.

    Thu, 06/17/2010 - 15:01 — SomNambul
    Authors: Erhan Bayraktar, Qingshuo Song, Yu-Jui Huang
    Subjects: Computational Finance
    Abstract

    Our goal is to resolve a problem proposed by Karatzas and Fernholz (2008):
    Characterizing the minimum amount of initial capital that would guarantee the
    investor to beat the market portfolio with a certain probability as a function
    of the market configuration and time to maturity. We show that this value
    function is the smallest supersolution of a non-linear PDE. As in Karatzas and
    Fernholz (2008), we do not assume the existence of an equivalent local
    martingale measure but merely the existence of a local martingale deflator.

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