Numerical Approximation for a Portfolio Optimizati

Authors: M’hamed Gaigi Vathana Ly Vath Mohamed Mnif Salwa Toumi

Publish Date: 2015/09/04

Volume: 74, Issue: 1, Pages: 163-195

PDF Link

Abstract

This paper concerns with numerical resolution of an impulse control problem under state constraints arising from optimal portfolio selection under liquidity risk and price impact We show that the value function could be obtained as the limit of an iterative procedure where each step is an optimal stopping problem and the reward function is related to the impulse operator Given the dimension of our problem and the complexity of its solvency region we use a numerical approximation algorithm based on quantization procedure instead of finite difference methods to calculate the value function the transaction and notransaction regions We also focus on the convergence of our numerical scheme in particular we show that it satisfies monotonicity stability and consistency properties We further enrich our studies with some numerical results for the optimal transaction strategyThis research benefitted from the support of the Chaire Marchés en Mutation Fédération Bancaire Française and the French ANR research grant LIQUIRISKThe authors thank two anonymous referees for their constructive comments which have led to a much improved version of the paper

Keywords: