A Study of Business Decisions Under Uncertainty: The Probability of the Improbable - With Examples from the Oil and Gas Exploration Industry

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Universal-Publishers, 2010 - Business & Economics - 408 pages
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This dissertation will discuss the uncertainty encountered in the daily operations of businesses. The concepts will be developed by first giving an overview of probability and statistics as used in our everyday activities, such as the basic principles of probability, univariate and multivariate statistics, data clustering and mapping, as well as time sequence and spectral analysis. The examples used will be from the oil and gas exploration industry because the risks taken in this industry are normally quite large and are ideal for showing the application of the various techniques for minimizing risk. Subsequently, the discussion will deal with basic risk analysis, spatial and time variations of risk, geotechnical risk analysis, risk aversion and how it is affected by personal biases, and how to use portfolios to hedge risk together with the application of real options. Next, fractal analysis and its application to economics and risk analysis will be examined, followed by some examples showing the change in the Value at Risk under Fractal Brownian Motions. Finally, a neural network application is shown whereby some of these risks and risk factors will be combined to forecast the best possible outcome given a certain knowledge base. The chapters will discuss: Basic probability techniques and uncertainty principles Analysis and diversification for exploration projects The value and risk of information in the decision process Simulation techniques and modeling of uncertainty Project valuation and project risk return Modeling risk propensity or preference analysis of exploration projects Application of fractals to risk analysis Simultaneous prediction of strategic risk and decision attributes using multivariate statistics and neural networks"
 

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Contents

Log normality
169
Uncertainty and Risk
174
The Magnitude of uncertainty
176
Technical Market Environmental and Political Risks
178
Independent multiple risk estimates
179
Reserve estimation
180
Production areas
184
Play assessment
185

Correlation Coefficient
32
Weighted Averages
33
Useful computations and formulas
34
Cumulative Distribution Shapes
36
Testing Normal Populations
37
Degrees of Freedom
39
The F Test
40
The Chi Squared Test
41
Simultaneous equations
42
Matrix multiplication
43
Matrix Inversion
44
Transpose of a Matrix
45
Determinants
46
Vector Space
47
Cramers Rule
48
Principal Component Analysis
52
Markov Chains and Matrices
56
Sequences of the same state
58
CHAPTER 2
60
Introduction
61
Uncertainty and Mapping Accuracy
66
Distribution of Points
68
Uniform Distribution
69
Gridding using Nearest Neighbor Method
71
Gridding using Inverse Distance Method
74
Gridding using Kriging and CoKriging
76
Gridding using Minimum Curvature
85
Gridding using Polynomial Regression
86
Gridding using the Radial Basis Function
88
Gridding using Shepards Method
90
Gridding using Triangulation
91
Contouring
92
Structural Noses
93
Regional Dip
94
Trend Surface Analysis
97
Contour Maps as Surfaces
98
Pitfalls in Trend Surfaces
105
CHAPTER 3
106
Introduction to Time Series Analysis
107
Taylor Series and MacLaurin Series
114
Linear Systems
115
Systems Obeying the Superposition Principle
116
Fourier Series
117
Euler Formula
118
Spectral Decomposition
119
Principle of Superposition
120
Convolution
122
Correlations
126
Filtering of time series
127
Linear Interpolation of points
129
Double Fourier and time series
132
Multivariate extensions of elementary statistics
138
Hotelling T Square Distribution
139
Discriminant Functions
140
Cluster Analysis
148
CHAPTER 4
151
Introduction to Risk and Uncertainty
152
Dependence and Independence
153
Decision Trees
154
Conditional Probability or Bayes Theorem
155
Stochastic Processes
157
Biases and Opinions
161
Chance of Success
163
Triangular Distribution
167
Play Risk
186
Play and Prospect Resource Estimates
190
Detailed Play Risk Analysis
199
Recovery factors
201
Economic profitability
202
Multiple prospective zones
213
Optimum Working Interest
220
CHAPTER 5
221
Introduction
222
von Neumann and Morgenstern
223
Small versus Large Gambles
226
Ellsberg paradox
229
Process Utilities and Regret Theory
230
Risk Aversion
231
Utility Functions and Statistics
236
Portfolios
242
Portfolio Analysis
246
Determining Working Interest
258
Incomplete probability information
270
The Law of Large Numbers
271
Decision Theory
273
Value of Information
274
Bayes Theorem and Terminal Action Cost
277
Minimization and Maximization
283
Risk Adjusted Value and Price Sensitivity
286
CHAPTER 5 APPENDIX
303
The Value of Money Discount Rates and Opportunity Costs
308
Discounted cash flow models
311
CHAPTER 6
314
Introduction
315
Old and New Paradigms
316
Real Options
319
Discrete simulation of uncertainty using the binary lattice approach
322
Option to Acquire Additional Information
330
Financial versus Real Options
336
Option to Delay or Timing Option
339
Option to Expand
342
Option to Abandon
343
Option uses
345
Option to Choose
346
The BlackScholes Model
347
Monte Carlo Simulations
349
CHAPTER 7
355
Introduction
356
Fractal Dimension
357
Hurst Exponent and Rescaling
359
RS and Financial Markets
360
Fractal Statistics
362
Fractal Analysis
365
Dynamical Systems
366
Hénon map
367
Fractal Application Example
370
Oil and Gas Example of Fractal Application
373
Artificial NeuralNetwork Paradigm
377
The Single Neuron as a Classifier
378
Basic Neural Network Concepts
379
Types of Networks
382
Network Learning
384
Hopfield Networks
387
Genetic Algorithm
389
Conclusion
392
References and Bibliography
394
Index
401
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