Minimax perfect stopping rules for selling an asset near its ultimate maximum

TL;DR

This paper introduces a minimax optimal stopping rule for selling an asset close to its maximum, characterized by a time-dependent threshold, improving previous strategies and applicable to various price models.

Contribution

The paper proposes a novel minimax perfect stopping rule based on a regret criterion, providing a unique optimal selling strategy that outperforms earlier methods.

Findings

The stopping rule is optimal in a minimax sense.

The rule is characterized by a time-dependent deviation threshold.

The approach applies to general price models.

Abstract

We study the problem of selling an asset near its ultimate maximum in the minimax setting. The regret-based notion of a perfect stopping time is introduced. A perfect stopping time is uniquely characterized by its optimality properties and has the following form: one should sell the asset if its price deviates from the running maximum by a certain time-dependent quantity. The related selling rule improves any earlier one and cannot be improved by further delay. The results, which are applicable to a quite general price model, are illustrated by several examples.