Performance analysis of the optimal strategy under partial information

Ahmed Belhadjayed (1, 2) , Grégoire Loeper (3) , Sofiene El Aoud (1, 2) , Frédéric Abergel (2, 1)

1 FiQuant - Chaire de finance quantitative
2 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
3 Monash University [Clayton]

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.

Domaines: Finance quantitative [q-fin.CP]; Gestion de portefeuilles [q-fin.PM]

Ahmed Belhadjayed, Grégoire Loeper, Sofiene El Aoud, Frédéric Abergel. Performance analysis of the optimal strategy under partial information. International Journal of Theoretical and Applied Finance, 2017, 20 (2), pp.1750016. ⟨10.1142/S0219024917500169⟩. ⟨hal-01512432⟩