Optimal trend following trading rules

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

Research output: Contribution to journalArticle

  • 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

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

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: Contribution to journalArticle

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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