### 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 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 language | English |
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Pages (from-to) | 560-578 |

Journal | Mathematical Finance |

Volume | 23 |

Issue number | 3 |

Early online date | 13 Feb 2012 |

DOIs | |

Publication status | Published - Jul 2013 |

### Keywords

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

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## Cite this

Zervos, M., Johnson, T., & Alazemi, F. (2013). Buy-low and sell-high investment strategies.

*Mathematical Finance*,*23*(3), 560-578. https://doi.org/10.1111/j.1467-9965.2011.00508.x