Numerical methods for an optimal order execution problem

This paper deals with numerical solutions to an impulse control problem arising from optimal portfolio liquidation with bid-ask spread and market price impact penalizing speedy execution trades. The corresponding dynamic programming (DP) equation is a quasi-variational inequality (QVI) with solvency constraint satisfied by the value function in the sense of constrained viscosity solutions. By taking advantage of the lag variable tracking the time interval between trades, we can provide an explicit backward numerical scheme for the time discretization of the DPQVI. The convergence of this discrete-time scheme is shown by viscosity solutions arguments. An optimal quantization method is used for computing the (conditional) expectations arising in this scheme. Numerical results are presented by examining the behaviour of optimal liquidation strategies, and comparative performance analysis with respect to some benchmark execution strategies. We also illustrate our optimal liquidation algorithm on real data, and observe various interesting patterns of order execution strategies. Finally, we provide some numerical tests of sensitivity with respect to the bid/ask spread and market impact parameters

Primary Productivity and Water Use of the Perennial Grass, Cenchrus Ciliaris, in Arid Environments

Cenchrus ciliaris is a perennial grass that may be suitable for the restoration of Rhanterium steppes (Chaieb et al., 1991). In this study, four Cenchrus ciliaris accessions from Tunisia from a range of climate and soil conditions, likely to vary in their adaptation to drought, were evaluated for productivity, rainuse-efficiency and reproductive output at Sfax in southern Tunisia. The suitability of these accessions for the restoration of Rhanterium steppes is considered

Numerical approximation for an impulse control problem arising in portfolio selection under liquidity risk

18 pagesWe investigate numerical aspects of a portfolio selection problem studied in [10], in which we suggest a model of liquidity risk and price impact and formulate the problem as an impulse control problem under state constraint. We show that our impulse control problem could be reduced to an iterative sequence of optimal stopping problems. Given the dimension of our problem and the complexity of its solvency region, we use Monte Carlo methods instead of finite difference methods to calculate the value function, the transaction and no-transaction regions. We provide a numerical approximation algorithm as well as numerical results for the optimal transaction strategy