Buying and selling an asset over the finite time horizon: A non-parametric approach

Abstract

We consider the problem of buying an asset and selling it later in the open market within a limited time-period. In such a situation, it is usually assumed that the market prices are random observations from a known distribution. However, we propose in the paper the rank-based trading strategy that does not require any distributional assumption. We only assume that the agent's utility depends on the actual ranks of the purchase and selling prices of the asset. The non-parametric trading policy, which maximizes the agent's expected utility, can be stated with a sequence of critical ranks; the agent must buy an asset at time j if the relative rank of its purchase price is larger than the pre-specified critical rank at that time. Likewise, the agent must sell the asset at time k if the relative rank of its selling price is less than the pre-specified critical rank at time k. Finally, we conduct a simulation experiment to analyze the effect of the auto-correlation in market prices on the performance of the optimal trading policy.