Performance Analysis of the Optimal Strategy Under Partial Information

20 Pages Posted: 13 Oct 2015

See all articles by Ahmed Bel Hadj Ayed

Ahmed Bel Hadj Ayed

BNP Paribas; Ecole Centrale Paris - Laboratory of Mathematics Applied to Systems

Gregoire Loeper

BNP Paribas; Monash University - School of Mathematical Sciences; Monash University - Monash Centre for Quantitative Finance and Investment Strategies; Ecole Polytechnique, Palaiseau - CMAP CNRS-UMR 7641 and Ecole Polytechnique

Sofiene El Aoud

Ecole Centrale Paris - Laboratory of Mathematics Applied to Systems

Frederic Abergel

BNP Paribas Asset Management; CentraleSupélec, Université Paris-Saclay

Date Written: October 13, 2015

Abstract

The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein-Uhlenbeck process. We focus on the optimal strategy with a logarithmic utility function under full or partial information. For both cases, we provide the asymptotic expectation and variance of the logarithmic return as functions of the signal-to-noise ratio and of the trend mean reversion speed. Finally, we compare the asymptotic Sharpe ratios of these strategies in order to quantify the loss of performance due to partial information.

Keywords: Optimal trading strategy, Kalman filter, Sharpe ratio, partial observations

Suggested Citation

Bel Hadj Ayed, Ahmed and Bel Hadj Ayed, Ahmed and Loeper, Gregoire and El Aoud, Sofiene and Abergel, Frederic, Performance Analysis of the Optimal Strategy Under Partial Information (October 13, 2015). Available at SSRN: https://ssrn.com/abstract=2673470 or http://dx.doi.org/10.2139/ssrn.2673470

Ahmed Bel Hadj Ayed (Contact Author)

Ecole Centrale Paris - Laboratory of Mathematics Applied to Systems ( email )

Grande Voie des Vignes
Châtenay-Malabry, 92290
France

BNP Paribas ( email )

Paris
France

Gregoire Loeper

BNP Paribas ( email )

Paris
France

Monash University - School of Mathematical Sciences ( email )

Clayton Campus
Victoria, 3800
Australia

Monash University - Monash Centre for Quantitative Finance and Investment Strategies ( email )

9 Rainforest Walk
Clayton Campus
Monash University, Victoria 3800
Australia

HOME PAGE: http://https://www.monash.edu/science/quantitative-finance

Ecole Polytechnique, Palaiseau - CMAP CNRS-UMR 7641 and Ecole Polytechnique ( email )

Route de Saclay
Palaiseau, 91128
France

Sofiene El Aoud

Ecole Centrale Paris - Laboratory of Mathematics Applied to Systems ( email )

Grande Voie des Vignes
Châtenay-Malabry CEDEX, 92290
France

Frederic Abergel

BNP Paribas Asset Management ( email )

Paris
France

CentraleSupélec, Université Paris-Saclay ( email )

Paris
France

HOME PAGE: http://www.mas.ecp.fr/fiQuant

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