Buy-low and sell-high investment strategies

Mihail Zervos, Timothy Johnson, Fares Alazemi

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)560-578
JournalMathematical Finance
Issue number3
Early online date13 Feb 2012
Publication statusPublished - Jul 2013


  • optimal investment strategies
  • optimal switching
  • sequential entry and exit decisions
  • variational inequalities


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