Browsing by Subject "Risk aversion"

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Approximations in decision analysis and their applications to shale field development
(2020-06-22) Beck, Andrew Alfred; Bickel, J. Eric; Hasenbein, John J.; Leibowicz, Benjamin D.; Pyrcz, Michael J.
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.
Model complexity and risk aversion in decision analysis
(2023-08-07) Small, Colin Andrew; Bickel, J. Eric; Leibowicz, Benjamin; Hasenbein, John; Dyer, James S.; Henry, Stephen
Models are often formulated to aid in decision-making. However, the details included or excluded are often determined with minimal examination of the effects. There is a tendency to make models more complex than merited. Yet, decision makers’ risk preferences are often ignored without considering the effect on recommendations. Additionally, modelers do not always understand the difference between preferences toward deterministic outcomes and risk preferences or the impact of modeling conflicting risk and deterministic preferences together in a single component. In this paper, I investigate the relationship between complexity and accuracy, using COVID-19 forecasting as a case study. I find our simple model is comparable in accuracy to highly publicized models, generating among the best-calibrated forecasts. This may be surprising, given the complexity of many high-profile models supported by large teams. However, it is consistent with research suggesting simple models perform very well in a variety of settings. Although utility functions are a fundamental component of decision analysis, they can assume many forms. For small decisions, the choice might not change the decision. But it can greatly affect recommendations for large decisions. There are qualitative recommendations on which functional form to use. But there is no quantitative recommendation relating size of uncertainties to choice of utility function. By maximizing error in certain equivalents when using different utility functions, this paper provides guidance into when to use different utility functions. Although decision makers should be approximately risk neutral for small problems, they are often “risk averse.” Rabin and Thaler showed utility functions modeling small-scale risk aversion result in absurd risk aversion for large uncertainties. They explain small-scale risk aversion is due to loss aversion, where pain from losses exceeds benefit from gains. But preferences for deterministic losses and gains is a deterministic preference and is not equivalent to risk preference. They argue loss aversion caused the observed behavior, yet modelled deterministic and risk preferences in a single factor. In this paper, I show modeling risk and deterministic preference separately can resolve Rabin’s Paradox, underscoring the need to explicitly model both when deterministic preferences can influence decision making or conflict with risk preferences.
Optimization approaches for energy infrastructure network design
(2021-05-08) Geetha Jayadev, Gopika; Leibowicz, Benjamin D.; Bard, Jonathan F.; Kutanoglu, Erhan; Rai, Varun
This dissertation focuses on applying operations research techniques to problems arising in the energy sector. The work presented attempts to push the existing frontiers in energy optimization by adding to an existing open-source framework in electricity infrastructure optimization and applying bilevel programming to relatively unexplored applications in natural gas market modeling. This dissertation consists of five chapters. Chapter 1 provides an introduction encompassing a brief description and motivation for the dissertation’s work. The future development of the U.S. electricity sector will be shaped by technological, economic, and policy drivers whose trajectories are highly uncertain. Chapter 2 describes an optimization model for the integrated generation and transmission system in the continental U.S., which is used to explore electricity infrastructure pathways from the present through 2050. By comparing and contrasting results from numerous scenarios and sensitivity settings, we ultimately affirm five key policy-relevant insights. (1) U.S. electricity can be substantially decarbonized at a modest cost, but complete decarbonization is very costly. (2) Significant expansion of solar PV and wind to combine for at least 40% of the generation mix by 2050 is fairly certain. However, solar PV and battery storage are more affected by economic and policy assumptions than wind. (3) Investments in long-distance transmission are minimal, while investments in battery storage are much more significant under a wide range of assumptions. (4) Optimal solutions include large investments in natural gas capacity, but gas capacity utilization rates decline steadily and significantly. (5) Cost structures shift away from operating expenditures and toward capital expenditures, especially under climate policy. We conclude our article by discussing the policy implications of these findings. Chapter 3 presents a bilevel programming model to aid decision-making in natural gas markets where multiple autonomous agents interact strategically, possibly with conflicting interests. In the proposed model, a liquefied natural gas (LNG) operator is the leader, and a natural gas (NG) producer is the follower. The LNG operator attempts to optimally locate LNG export terminals, purchase gas from the NG producer, and export it as LNG. The NG producer aims to optimize production, pipeline investments, and sales to domestic consumers and the LNG operator. To solve the bilevel problem, we first reformulate it as a single-level problem by exploiting the lower-level problem’s convexity. Then, we use disjunctive reformulations of complementarity constraints and piecewise linear approximations of objective function terms to convert the problem into a convex quadratic mixed-integer program (QMIP). Computational experiments confirm that the QMIP is tractable and can be solved efficiently. We apply our bilevel framework to a case study of the Gulf-Southwest region of the United States and evaluate several decision-making scenarios. The scenario results emphasize the importance of using the bilevel methodology to anticipate the effects of new LNG export facilities on NG prices across the domestic gas network. Adding these large gas-consuming facilities at specific locations puts upward pressure on domestic gas prices, although this is somewhat mitigated by the NG producer’s optimal production response to the increased demand. Chapter 4 presents a risk-based integer bilevel programming model that considers two players in a leader-follower setting, where each tries to maximize their individual profits. The leader or manufacturer makes decisions pertaining to facility location and the amount of raw material to buy from the supplier. The supplier or follower decides how much raw material to produce. Both players face demand uncertainty in their respective markets while making investment, production, and sales decisions. We develop models for optimal decision-making under risk-neutral and risk-averse objectives and explore the effects of different risk attitudes on the problem and its optimal solution. These problems are hard to solve as the number of scenarios increase, and solving them generally involves developing customized algorithms. To find feasible solutions to the resulting stochastic bilevel problem, an algorithm is developed that iteratively solves a restricted version of the problem to obtain feasible solutions to the original problem. Extensive computational experiments are performed to evaluate algorithmic tractability and solution quality. The proposed algorithm is able to find high-quality feasible solutions to the bilevel problem in a very reasonable amount of time, and the attained solutions are found to be close to the optimal solution. The methodology is demonstrated with an example that addresses strategic issues in the natural gas market. The model considers two players, the liquefied natural gas (LNG) operator or leader and the natural gas (NG) producer or follower acting in a leader-follower setting. The LNG operator makes decisions pertaining to the locations of LNG facilities and the amount of gas to buy from the producer. The follower decides how much gas to produce. Both players face demand uncertainty in their respective markets and make investments, production, and sales decisions. The case study explores the Gulf-Southwest region of the United States and demonstrates the impact of the risk-averse decision-making approach on investment and operational decisions. Chapter 5 concludes this dissertation by summarizing the most important findings from each study and outlining valuable directions for future research.