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math.AP2018
Asymptotics for Small Nonlinear Price Impact: a PDE Approach to the Multidimensional Case
Erhan Bayraktar, Thomas Caye, Ibrahim Ekren
We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small non-linear price impact. In our model cross-…
math.AP2016
Existence of invariant measures for the stochastic damped Schrödinger equation
Ibrahim Ekren, Igor Kukavica, Mohammed Ziane
In this paper, we address the long time behaviour of solutions of the stochastic Schrodinger equation in . We prove the existence of an invariant measure and establis…
math.AP2016
Pseudo Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs
Ibrahim Ekren, Jianfeng Zhang
In this paper we propose a new type of viscosity solutions for fully nonlinear path dependent PDEs. By restricting to certain pseudo Markovian structure, we remove the uniform non-…