Approximations in decision analysis and their applications to shale field development




Beck, Andrew Alfred

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Every decision analysis must strike a balance between cogency and verisimilitude. This is particularly challenging in the development of shale oil and gas assets, which are portfolios of options under price and production uncertainties. Decision makers maximize net present value by making periodic investment decisions, alternating between deciding which wells and infrastructure to invest in, and learning about the production and price environment. Current decision support tools are very simple, usually consisting of decision trees, fixed price decks, and no midstream constraints. Current optimization techniques are only applicable to very small, simplified problems. In this dissertation, we improve upon current techniques. We develop a heuristic that maps the current information of an asset, such as inventory, prices, and estimated production to a well schedule. The heuristic can be combined with optimization routines, decision trees, or strategy tables to improve decision quality and asset valuation. Next, we model a shale asset as a Markov Decision Process, allowing us to solve problems of a similar size and complexity to the state-of-the-art optimization techniques via dynamic programming. We compare the performance of the heuristic to the optimal solution on a set of small example problems, showing that its performance is comparable. Then we compare the performance of the heuristic to the decision tree method on a large example problem, showing that the heuristic performs significantly better. All decision makers are risk averse when the stakes get large enough. The literature gives general, qualitative recommendations about when to formally model risk aversion, but the recommendations are not specific enough. We develop a set of theoretical results on when an expected value analysis is sufficient, when an exponential utility analysis is sufficient, and when an analyst needs to use a non-CARA utility function that includes the decision maker’s entire portfolio. We use the Pearson distribution system and historical data from the S&P 500 to develop a representative set of alternatives over wealth that a decision maker might face in practice. We use our theoretical results to study our set of alternatives and derive a clear recommendation of when to use different utility models. We summarize our results in the “7-9-11” rule of thumb. If the alternatives in a decision problem are left-skewed, symmetric, or right-skewed, and the standard deviation of the returns is less than 7%, 9%, or 11% of the decision maker’s wealth, respectively, then an expected value analysis is sufficient, as formally modeling risk aversion will not have a material effect on the decisions. We also provide recommendations of when to move beyond an exponential utility function to a more accurate, non-CARA representation of utility, such as the linear-exponential utility function. Finally, we apply risk aversion to the shale asset management problem and explore the impact different risk tolerances have on decision making. We show that the more risk averse a decision maker is, the less she will invest. This suggests a certain minimum risk tolerance as a pre-requisite to investing in a shale asset. However, because individual decisions in shale are very small relative to the overall value of shale assets, introducing risk aversion has a limited effect overall on asset value.


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