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On a stochastic differential equation arising in a price impact model

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posted on 2013-01-01, 00:00 authored by Peter Bank, Dmitry KramkovDmitry Kramkov

We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in the price impact model developed by Bank and Kramkov (2011) [1] and [2]. These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments.

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Publisher Statement

This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.spa.2012.10.011

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2013-01-01

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    Keywords

    Clark-Ocone formulalarge investorMalliavin derivativePareto allocationprice impactSobolev embeddingstochastic differential equation.Mathematical Sciences not elsewhere classified

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