# Market Theories

Stochastic process | Description | Applicability to real markets | Notes |
---|---|---|---|

diffusion process | satisfies the diffusion equation | poor | Regnault (1863) and Osborne (1959) discovered that price deviation is proportional to the square root of time, but the nonstationarity found by Houthakker (1961) and Osborne (1962) compromises the significance of the process. |

Gaussian process | increments normally distributed | poor | Financial markets exhibit leptokurtosis (Mitchell (1915, 1921), Olivier (1926), Mills (1927), Osborne (1959), Larson (1960), Alexander (1961)). |

Lévy process | stationary independent increments | poor | Houthakker (1961) and Osborne (1962) found nonstationarities in markets in the form of positive autocorrelation in the variance of returns. |

Markov process | memoryless | poor | Houthakker (1961) and Osborne (1962) found positive autocorrelation in the variance of returns. |

martingale | zero expected return | submartingale: good for stock market | Bachelier (1900) and Samuelson (1965) recognised the importance of the martingale in relation to an efficient market. Whilst Cox and Ross (1976), Lucas (1978) and Harrison and Kreps (1979) pointed out that in practice investors are risk averse, so (presumably as compensation for the time value of money and systematic risk) they demand a positive expected return. In a long-only market like a stock market this implies that the price of a stock follows a submartingale (a martingale being a special case when investors are risk-neutral). |

random walk | discrete version of Brownian motion | poor | LeRoy (1973) and (especially) Lucas (1978) pointed out that a random walk is neither necessary nor sufficient for an efficient market. |

Wiener process/Brownian motion | continuous-time, Gaussian independent increments | poor | Bachelier (1900) developed the mathematics of Brownian motion and used it to model financial markets. Note that Brownian motion is a diffusion process, a Gaussian process, a Lévy process, a Markov process and a martingale. On the one hand this makes it a very strong condition (and therefore the least realistic), on the other hand it makes it a very important “generic” stochastic process and is therefore used extensively for modelling financial markets (for example, see Black and Scholes (1973)). |

Graphical Theories

- Breakout theory
- Candlestick psychology
- Clayburg theory
- Indicators combined
- Ross theory
- Wolf theory
- Dacharts

- Angles method
- Crane theory
- Carney theory
- Di Napoli theory
- Fractal theory
- Gann theory
- Pesavento theory
- Pyrapoint
- Sacred geometry
- Symmetry & Swing
- Cycle Studies
- Clyde Lee method

Geometrical Theories

- Constant application
- Murrey Math theory
- Personal numerical theory
- sacred numbers & ratio
- moonXmoon theory
- signXsign theory
- seasonXseason theory
- moonXsign theory
- combined X combined theory
- mml-x-moon theory

Numerical Theories

- FFT theory
- Mesa theory
- Neural Nets theory
- Time & Space theory
- Quantum method
- General Statistical Methods
- Fisher Transform method
- Monte Carlo Methods
- Chaos Trading B.Williams

Mathematical & Physical Theories

- Astrotides
- Berg theory
- Cycle theory
- Delta theory
- Fishtrading method
- Ions theory
- Larson theory
- Moon theory
- Solar-Terrestrial theory
- WavesAstrology theory
- harmonics method
- cosmo-trend application
- Astro-NeuralNets Alphee Theory
- Astro Cycles Research
- 56 Year Cycle McMinn

Astro & Terrestrial Theories

- Physics of Finance
- Quantitative Finance
- Mathematical statistics and Econometry
- Chaos& Non Linear Dynamics Models
- Complex Systems in Financial Market
- Finance and Time Series
- Gauge Physics of Finance

Econophysics

- Financial Engineering
- Mathematical Models in Finance
- Market Models
- Mathematical Models for Trading
- Genetic Algorithms for trading
- Neural Network Trading Models
- Bayesian Networks Applications
- Financial Forecasting with Support Vector Machines
- Computational Methods for Financial Applications
- Gauge geometry of financial markets
- Quantum Electrodynamics Analogy
- Mesoscopics of stock market
- Path Integrals Financial Markets
- Quantum Finance
- Dynamic Models
- Brownian motion stock markets
- Option Theory Stochastic Analysis
- Option Pricing under Quantum Theory
- Microscopic Models of Financial Markets
- Intelligent Finance

Theories Combined- Forecast & Lessons Miscellaneous