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Peter Imkeller

  1. The Existence of Dominating Local Martingale Measures.

    Чт, 11/17/2011 - 15:01 — SomNambul
    Authors: Peter Imkeller, Nicolas Perkowski
    Subjects: Probability
    Abstract

    We prove that for locally bounded processes, the absence of arbitrage of the
    first kind is equivalent to the existence of a dominating local martingale
    measure. This is related to results from the theory of filtration enlargements.

  2. Differentiability of quadratic BSDEs generated by continuous martingales.

    Ср, 08/04/2010 - 15:01 — SomNambul
    Authors: Peter Imkeller, Anthony Reveillac, Anja Richter
    Subjects: Probability
    Abstract

    In this paper we consider a class of BSDEs with drivers of quadratic growth,
    on a stochastic basis generated by continuous local martingales. We first
    derive the Markov property of a forward-backward system (FBSDE) if the
    generating martingale is a strong Markov process. Then we establish the
    differentiability of a FBSDE with respect to the initial value of its forward
    component. This enables us to obtain the main result of this article, namely a
    representation formula for the control component of its solution.

  3. Results on numerics for FBSDE with drivers of quadratic growth.

    Ср, 04/14/2010 - 15:01 — SomNambul
    Authors: Peter Imkeller, Gonçalo dos Reis, Jianing Zhang
    Subjects: Pricing of Securities
    Abstract

    We consider the problem of numerical approximation for forward-backward
    stochastic differential equations with drivers of quadratic growth (qgFBSDE).
    To illustrate the significance of qgFBSDE, we discuss a problem of cross
    hedging of an insurance related financial derivative using correlated assets.
    For the convergence of numerical approximation schemes for such systems of
    stochastic equations, path regularity of the solution processes is
    instrumental. We present a method based on the truncation of the driver, and
    explicitly exhibit error estimates as functions of the truncation height.

  4. Path regularity and explicit convergence rate for BSDE with truncated quadratic growth.

    Ср, 10/28/2009 - 16:01 — SomNambul
    Authors: Peter Imkeller, Goncalo dos Reis
    Subjects: Probability
    Abstract

    We consider backward stochastic differential equations with drivers of
    quadratic growth (qgBSDE). We prove several statements concerning path
    regularity and stochastic smoothness of the solution processes of the qgBSDE,
    in particular we prove an extension of Zhang's path regularity theorem to the
    quadratic growth setting. We give explicit convergence rates for the difference
    between the solution of a qgBSDE and its truncation, filling an important gap
    in numerics for qgBSDE.

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