Optimal trend following trading rules

Min Dai, Zhou Yang, Qing Zhang, Qiji Jim Zhu

Research output: Research - peer-reviewArticle

  • 2 Citations

Abstract

This paper is concerned with the optimality of a trend following trading rule. The underlying market is modeled like a bull-bear switching market in which the drift of the stock price switches between two states: The uptrend (bull market) and the down trend (bear market). We consider the case when the market mode is not directly observable and model the switching process as a hidden Markov chain. This is a continuation of our earlier study reported in Dai et al. [Dai M, Zhang Q, Zhu Q (2010) Trend following trading under a regime-switching model. SIAM J. Fin. Math. 1:780-810] where a trend following rule is obtained in terms of a sequence of stopping times. Nevertheless, a severe restriction imposed in Dai et al. [Dai M, Zhang Q, Zhu Q (2010) trend following trading under a regime-switching model. SIAM J. Fin. Math. 1:780-810] is that only a single share can be traded over time. As a result, the corresponding wealth process is not self-financing. In this paper, we relax this restriction. Our objective is to maximize the expected log-utility of the terminal wealth. We show, via a thorough theoretical analysis, that the optimal trading strategy is trend following. Numerical simulations and backtesting, in support of our theoretical findings, are also reported.

LanguageEnglish (US)
Pages626-642
Number of pages17
JournalMathematics of Operations Research
Volume41
Issue number2
DOIs
StatePublished - May 1 2016

Fingerprint

Trends
Trading rules
Market
Regime-switching Model
Restriction
Regime-switching model
Wealth
Markov processes
Switches
Computer simulation
Hidden Markov Chain
Trading Strategies
Stopping Time
Stock Prices
Optimal Strategy
Continuation
Switch
Optimality
Theoretical Analysis
Maximise

Keywords

  • Bull-bear switching model
  • Hamilton-jacobi-bellman equations
  • Partial information
  • Trend following trading rule

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

Cite this

Optimal trend following trading rules. / Dai, Min; Yang, Zhou; Zhang, Qing; Zhu, Qiji Jim.

In: Mathematics of Operations Research, Vol. 41, No. 2, 01.05.2016, p. 626-642.

Research output: Research - peer-reviewArticle

Dai, M, Yang, Z, Zhang, Q & Zhu, QJ 2016, 'Optimal trend following trading rules' Mathematics of Operations Research, vol 41, no. 2, pp. 626-642. DOI: 10.1287/moor.2015.0743
Dai M, Yang Z, Zhang Q, Zhu QJ. Optimal trend following trading rules. Mathematics of Operations Research. 2016 May 1;41(2):626-642. Available from, DOI: 10.1287/moor.2015.0743
Dai, Min ; Yang, Zhou ; Zhang, Qing ; Zhu, Qiji Jim. / Optimal trend following trading rules. In: Mathematics of Operations Research. 2016 ; Vol. 41, No. 2. pp. 626-642
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