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![Page 1: On Stochastic Multi Criteria Decision Analytics and Artificial Intelligence for Efficient Stock Trading By Gordon H. Dash, Jr. 1, Nina Kajiji 2, John Forman.](https://reader037.fdocuments.in/reader037/viewer/2022110323/56649d8c5503460f94a74854/html5/thumbnails/1.jpg)
On Stochastic Multi Criteria Decision Analytics and Artificial Intelligence for Efficient Stock
Trading
By
Gordon H. Dash, Jr.1, Nina Kajiji2, John Forman3
1College of Business, University of Rhode Island2Center for School Improvement and Social Policy, University of
Rhode Island3Thomson-Reuters, Boston, MA
www.GHDash.net Preliminary
X111 International ConferenceApplied Stochastic Models and Data Analysis
June 30 – July 3, 2009
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Justification
Increasing complexities of global markets
New mathematical modeling of stock price behavior gaining popularity
Traditional Brownian Motion Model assume stock price follow a random walk
Geometric Brownian Motions assumes stock returns follow a random walk
Stochastic methods are gaining popularity since they rely upon random and pseudorandom methods to define an asset’s price
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Objective
To join stochastic multi-criteria decision analytics with neural network based modeling to assign expected stocks to classification groups based on their trading profitability.
To examine the time-series efficiency of the DK4-AT via a double log (restricted Cobb-Douglas (CD)) production model
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A Trading System
Factors that define a trading system are: An identification of the markets to trade Position quantities to buy/sell Entry and exit decision that indicate when to
buy/sell When to exit a winning (losing) position
DK4-AT incorporates any number of advanced trading rules that conform to these factor decisions
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The Stock Trading Model
Shreve (2004) provides the framework for use of the stochastic integral to characterize uncertain stock trading. Specifically: Define the random variable Xt of a stock’s
market price, at time t. The probability space (Ω,Ѵ,Р), a measure space with P(Ω) = 1, as well as filtration.
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The Model (cont)
That is, Гi is loosely viewed as the set of events whose outcomes are certain to be revealed to investors as true or false by, or at, time t.
For any event, A, the probability assigned to A by investors is P(A). The price process X is said to be adapted if for all t, Xt is Vt measurable
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The Trading Strategy
We assumes a market that is not characterized by the no-risk unlimited profit arbitrage effects of trading on advanced knowledge.
We define a trading strategy θ that determines the quantity θt(ω) of each security held in each state ω Є Ω and at each time t.
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The Relation
Hence, given a price process X and a trading strategy θ that satisfies the no arbitrage conditions, the total financial gain between any times s and t ≥ s is defined as a stochastic integral
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Buy-Hold Strategy
A short-horizon element of the DK4-AT trading strategy captured by θ where an investor initiates a position immediately after some stopping time T and closes it at some later stopping time U.
Thus for a position size that is Vt measurable, the trading strategy θ is defined by θ = 1(T< t ≤ U) and the gain is:
.
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The n-dimensional Trading Strategy
Therefore, for n different securities, with price process X1 ,…, Xn the investor can choose an associated n-dimensional trading strategy θ = {θ1 ,…, θn} or some allowable set Ѳ, for which the total gain-from-trade process is:
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Why ANN?
Prediction capabilities of ANNs for high frequency stock market (Refenes, 1996)
Neural networks do not require a parametric system model
They are relatively insensitive to chaotic data patterns
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The RBF ANN Topology
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AT Algorithm
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Production System for a Profitable Stock
Pick a starting date – Case Study List Creation Date: 24-Jan-2009
Establish historical period: 01-Jan-2008 through 1-Jan-2009, inclusive.
Create research sample (SAM): Number of trades ≥ 25 throughout the historical period. Identify tickers where 50% or more of the trades generated a dollar profit. Identify the research sample → 915 securities.
For SAM, obtain stock fundamentals (source: Yahoo) EPS – estimate current year Market Capitalization 52Wk Range – real time Percent change from 50 day Moving Average Average Daily Volume EPS estimate next year EPS estimate next quarter Day’s Range
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Production System for a Profitable Stock
Execute K-SOM Target variable: Number of Positive Trades for the ith security Predictor variables: fundamentals 1x1 classification structure – primarily to obtain distance measure Create weighted probability of profitable trade – that is, % profitable x distance
Use K4 to estimate the CD production of the weighted probability of positive trades
Use K4 with softmax transfer function Identify production elasticity for each fundamental variable Interpret the returns to scale for profitable trading
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ResultsNumber of Positive Trades by Security
1,00191081972863754645536427318291
72
66
60
54
48
42
36
30
24
18
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ResultsKSOM Centroid Distance – First 819 Securities
89181072964856748640532424316281
0.30
0.25
0.20
0.15
0.10
0.05
0.00
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ResultsK4 Analysis Using Softmax Transfer Function
Dependent Variable: Weighted % Positive TradesIndependent Variables: Ln(Fundamental Variable)
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ResultsPlot of Actual and Predicted of Weighted % Positive Trades using K4
Actual Predicted
1,00191081972863754645536427318291
9
6
3
0
-3
-6
-9
-12
-15
-18
-21
-24
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ResultsZoom in View – Actual and Predicted
Actual Predicted
455
-3
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ResultsWeights from Comparative K4 Models
Dependent Variable: Weighted % Positive Trades
Model Chosen – Norm2
An increase in the 52 Wk Range or the Day’s Range increases the Weighted % Positive Trades. That is, higher the price differential higher the profit potential
Mkt. Cap also exhibits a positive relationship. That is, higher the mkt. cap the higher the stock’s propensity to trade.
The other five variables all have a negative relationship to Weighted % Positive Trades.
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Pseudo Elasticity EstimatesPTCP: % Positive Trades weighted by K-SOM Centroid Proximity
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Conclusions
The production system exhibits decreasing returns to scale (0.338); hence, a simultaneous 1% change in all fundamentals will result in a .34% increase in the % of weighted profitable trades (volatility is good).
The DK4-AT proved to be an efficient “engine” for predicting high-frequency stock trades.
A K-SOM 20-Minute Cluster produce Centroid proximity scores the weighted the % profitable trade in a meaningful manner for prediction estimation.
A double-log (restricted CD) production function estimated by the K4 RBF with Norm:2 data transformation on fundamental variables produced meaningful production elasticity estimates