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  • Journal article
    Zheng H, 2009,

    Efficient frontier of utility and CVaR

    , MATHEMATICAL METHODS OF OPERATIONS RESEARCH, Vol: 70, Pages: 129-148, ISSN: 1432-2994
  • Journal article
    Westray N, Zheng H, 2009,

    Constrained nonsmooth utility maximization without quadratic inf convolution

    , STOCHASTIC PROCESSES AND THEIR APPLICATIONS, Vol: 119, Pages: 1561-1579, ISSN: 0304-4149
  • Journal article
    Cass T, 2009,

    Smooth densities for solutions to stochastic differential equations with jumps

    , Stochastic Processes and their Applications, Vol: 119
  • Journal article
    Brody DC, Davis MHA, Friedman RL, Hughston LPet al., 2009,

    Informed traders

    , Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 465, Pages: 1103-1122, ISSN: 1364-5021

    An asymmetric information model is introduced for the situation in which there is a small agent who is more susceptible to the flow of information in the market than the general market participant, and who tries to implement strategies based on the additional information. In this model market participants have access to a stream of noisy information concerning the future return of an asset, whereas the informed trader has access to a further information source which is obscured by an additional noise that may be correlated with the market noise. The informed trader uses the extraneous information source to seek statistical arbitrage opportunities, while at the same time accommodating the additional risk. The amount of information available to the general market participant concerning the asset return is measured by the mutual information of the asset price and the associated cash flow. The worth of the additional information source is then measured in terms of the difference of mutual information between the general market participant and the informed trader. This difference is shown to be nonnegative when the signal-to-noise ratio of the information flow is known in advance. Explicit trading strategies leading to statistical arbitrage opportunities, taking advantage of the additional information, are constructed, illustrating how excess information can be translated into profit.
  • Journal article
    Cass T, Friz P, Victoir N, 2009,

    Non-degeneracy of Wiener functionals arising from rough differential equations

    , Transactions of the American Mathematical Society, Pages: 3359-3371
  • Journal article
    FORDE MARTIN, JACQUIER ANTOINE, 2009,

    SMALL-TIME ASYMPTOTICS FOR IMPLIED VOLATILITY UNDER THE HESTON MODEL

    , International Journal of Theoretical and Applied Finance, Vol: 12, Pages: 861-876

    We rigorize the work of Lewis (2007) and Durrleman (2005) on the small-time asymptotic behavior of the implied volatility under the Heston stochastic volatility model (Theorem 2.1). We apply the Gärtner-Ellis theorem from large deviations theory to the exponential affine closed-form expression for the moment generating function of the log forward price, to show that it satisfies a small-time large deviation principle. The rate function is computed as Fenchel-Legendre transform, and we show that this can actually be computed as a standard Legendre transform, which is a simple numerical root-finding exercise. We establish the corresponding result for implied volatility in Theorem 3.1, using well known bounds on the standard Normal distribution function. In Theorem 3.2 we compute the level, the slope and the curvature of the implied volatility in the small-maturity limit At-the-money, and the answer is consistent with that obtained by formal PDE methods by Lewis (2000) and probabilistic methods by Durrleman (2004).
  • Journal article
    Sabir I, Fraser J, Cass T, Huang C, Grace Aet al., 2007,

    A quantitative analysis of the effect of cycle length on arrthymogenicity in hypokaleamic Langendorff-perfused murine hearts

    , Pflugers Archiv-European Journal of Physiology, Vol: 6, Pages: 925-936

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