Buy‐Low and Sell‐High Investment Strategies

19 Pages Posted: 9 Jun 2013

See all articles by Mihail Zervos

Mihail Zervos

King's College London - Department of Mathematics

Timothy C. Johnson

Heriot-Watt University - Maxwell Institute for Mathematical Sciences

Fares Alazemi

Kuwait University

Date Written: July 2013

Abstract

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 , 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 , e.g., if 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 , e.g., if 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.

Keywords: optimal investment strategies, optimal switching, sequential entry and exit decisions, variational inequalities

Suggested Citation

Zervos, Mihail and Johnson, Timothy C. and Alazemi, Fares, Buy‐Low and Sell‐High Investment Strategies (July 2013). Mathematical Finance, Vol. 23, Issue 3, pp. 560-578, 2013, Available at SSRN: https://ssrn.com/abstract=2276601 or http://dx.doi.org/10.1111/j.1467-9965.2011.00508.x

Mihail Zervos (Contact Author)

King's College London - Department of Mathematics ( email )

Strand
Strand
London, WC2R 2LS
United Kingdom

Timothy C. Johnson

Heriot-Watt University - Maxwell Institute for Mathematical Sciences ( email )

Edinburgh, Scotland EH14 4AS
United Kingdom

HOME PAGE: http://www.ma.hw.ac.uk/~timj/

Fares Alazemi

Kuwait University

Safat, 13060
Kuwait

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