# A Mathematical Analysis of Technical Analysis

@article{Lorig2019AMA, title={A Mathematical Analysis of Technical Analysis}, author={Matthew J. Lorig and Zhou Zhou and Bin Zou}, journal={Applied Mathematical Finance}, year={2019}, volume={26}, pages={38 - 68} }

ABSTRACT In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modelled by either an Ornstein-Uhlenbeck process or a two-state continuous-time Markov chain. For the case of an Ornstein-Uhlenbeck drift, we carry out several Monte Carlo experiments in order to… Expand

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#### References

SHOWING 1-10 OF 40 REFERENCES

Optimal trading strategy for an investor: the case of partial information

- Mathematics
- 1998

We shall address here the optimization problem of an investor who wants to maximize the expected utility from terminal wealth. The novelty of this paper is that the drift process and the driving… Expand

Trend Following Trading under a Regime Switching Model

- Economics, Computer Science
- SIAM J. Financial Math.
- 2010

The bull and bear phases of the markets are characterized mathematically using the conditional probabilities of the bull market given the up to date stock prices and the optimal buying and selling times are given in terms of a sequence of stopping times determined by two threshold curves. Expand

Optimal Trend Following Trading Rules

- Mathematics, Computer Science
- Math. Oper. Res.
- 2016

It is shown, via a thorough theoretical analysis, that the optimal trading strategy is trend-following, and the expected log-utility of the terminal wealth is maximize. Expand

Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain

- Economics, Computer Science
- Finance Stochastics
- 2004

A multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as a continuous time Markov chain with finitely many states is considered. Expand

Portfolio optimization with Markov-modulated stock prices and interest rates

- Computer Science, Mathematics
- IEEE Transactions on Automatic Control
- 2004

This work investigates the problem of maximizing the expected utility from terminal wealth and solves it by stochastic control methods for different utility functions by comparing the value function of the problem to one where the authors have constant (average) market data. Expand

Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case

- Mathematics
- 1969

OST models of portfolio selection have M been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model… Expand

Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets

- Economics
- Journal of Financial and Quantitative Analysis
- 2002

Abstract This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting returns. Previous solutions either require… Expand

Optimal consumption and portfolio policies when asset prices follow a diffusion process

- Economics
- 1989

Abstract We consider a consumption-portfolio problem in continuous time under uncertainty. A martingale technique is employed to characterize optimal consumption-portfolio policies when there exist… Expand

Utility maximization with partial information

- Mathematics
- 1995

In the present paper we address two maximization problems: the maximization of expected total utility from consumption and the maximization of expected utility from terminal wealth. The price process… Expand

A Dynamical Analysis of Moving Average Rules

- Economics
- 2004

The methods of various moving average rules remain popular with financial market practitioners. These rules have recently become the focus of empirical studies. However there seem to have been very… Expand