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

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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 |

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### Common terms and phrases

analysis applied asset behavior binomial Black-Scholes Brownian Motion cash flow certainty equivalent chance chapter clusters component compute contour cost covariance covariance matrix curve data points data set Decision Tree defined deterministic discount drilling economic Efficient Market Hypothesis eigenvectors equation estimate evaluation example expected value exploration Fourier Fractal frequency geologic grid spacing Hénon map Hopfield network Hurst exponent hydrocarbon input investment Kriging kurtosis linear log normal logarithmic lognormal matrix mean method million Monte Carlo simulation Neural Network node normal distribution oil and gas option value outcome parameters Pareto distributions plot porosity portfolio present value probability produce prospect random real option regression reservoir result risk aversion sample seismic data sequence shown in figure squares standard deviation statistical stochastic success trap trend surface uncertainty utility function variable variance Variogram vector volatility zero σ σ