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Buy-low and sell-high investment strategies

Zervos, Mihail ORCID: 0000-0001-5194-6881, Johnson, Timothy C. and Alazemi, Fares (2013) Buy-low and sell-high investment strategies. Mathematical Finance, 23 (3). pp. 560-578. ISSN 0960-1627

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Identification Number: 10.1111/j.1467-9965.2011.00508.x


Buy-low and sell-high investment strategies are a recurrent theme in the considerations of many investors. In this paper, we consider an investor who aims at maximizing the expected discounted cash-flow that can be generated by sequentially buying and selling one share of a given asset at fixed transaction costs. We model the underlying asset price by means of a general one-dimensional Itô diffusion X, we solve the resulting stochastic control problem in a closed analytic form, and we completely characterize the optimal strategy. In particular, we show that, if 0 is a natural boundary point of X, e.g., if X is a geometric Brownian motion, then it is never optimal to sequentially buy and sell. On the other hand, we prove that, if 0 is an entrance point of X, e.g., if X is a mean-reverting constant elasticity of variance (CEV) process, then it may be optimal to sequentially buy and sell, depending on the problem data.

Item Type: Article
Official URL:
Additional Information: © 2012 Wiley Periodicals
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 08 Aug 2012 13:13
Last Modified: 20 Sep 2021 02:49

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