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decision making under uncertainty models

The loss L(θ, a) is the difference between the utility of the consequence of the action for state θ, and the utility of the consequences of the best action for that state (or the lowest upper bound if the best action cannot be achieved). The goal is to find the optimal set of ‘hedges’, I.e. Methods of Decision Making under Uncertainty Maximin Criterion: This criterion, also known as the criterion of pessimism, is used when the decision-maker is... Maximax Criterion: This criterion, also known as the criterion of optimism, is used when the decision-maker … Given these three axioms (and some other technical assumptions), insurance policy A will be chosen over policy B if and only if EAU > EBU (where EiU is the linear expected utility associated with policy i). With COVID-19, … Similarly, we have a forecast for the amount of electricity the facility will use next August (also based on fitting a model to historical data), and we have a model for the distribution of actual consumption around the forecast. (But you have a better chance of doing this as an ad hoc exercise than by looking for tail outcomes in a model intended to be applicable generally.). But yeah, I, too, am leaning towards heuristics. In this case, the probability of receiving nothing from the low-payoff bet when the high-payoff bet would have yielded a prize is zero, while the probability of receiving nothing from the low-payoff bet when the low-payoff bet would have yielded a prize is 0.2. Careful specification of the functions u and π is critical to sound decision making. William F. Meehan III Contributor. That’s why I’m a fan of scenario analysis, at least as a first step. It’s also hard to make sure you’ve hired the *right* people, and that they have the right incentives. I.e. We present a scalable methodology to support large scale investments under uncertainty. So we’ve started working on how to do the multi-facility, multi-month generalization of the problem we’ve already solved…and it’s a bit of a mess. P. Fishburn, in International Encyclopedia of the Social & Behavioral Sciences, 2001, Conjoint measurement is used extensively for multiattribute outcomes in decision under risk and uncertainty (Keeney and Raiffa 1976). This seems like a reasonably cost effective way to generate two points of comparison. In this podcast, he talks about you’re issue, and how his group creates solutions. We are looking for a method of making these decisions. it might be difficult to even figure out what the consumption will be. We are not trying to beat the market. Decision-making under uncertainty: heuristics vs models. I am part of a three-person consulting team that is advising the company. Badaboom. At best they are valuable, high-maintenance inputs to an expert. Mostly no problem, but a tail event leads to catastrophe. Nothing in this article should be interpreted as … If I were overseeing such a project I think I’d go simple first and get more complicated as need demands. Downloadable! Posted by Phil on 14 ... (or equivalently stochastic harvesting models). the planning to consume part might well be the most important portion of the model as this involves altering business operations and has unique components well beyond what a pure trader deals with. On the other hand, you can probably estimate how uncertain are these parameters and when fed to the model how uncertain would be the outcomes. Explore the latest questions and answers in Decision Making Under Uncertainty, and find Decision Making Under Uncertainty experts. Such “black swans” pose a real challenge. You ask “How encompassing can you make your set of correlation models that will spit out synthetic data that “looks like” the realworld data that you have and expect?” That’s the right question, and the answer is that I have no faith that we can do this, largely because we don’t really know what we expect. Even for a single facility it’s hard to know exactly how to model all of this: we only have a few years of useful data — because both the facilities and the electric industry itself have changed a lot in the past five years, and are continuing to change — so that’s only a couple of dozen summer months for example. We need the variance-covariance matrix for the errors in the predicted prices between the facilities, and the variance-covariance matrix for the errors in the predicted electric load between the facilities, and we don’t have nearly enough data to estimate those with any confidence. Saptarshi. One thing that struck me reading your post is that you only have a few years of useful data given how much the company and the market have changed and are continuing to change. If what you’re saying is that we’d be fools to think we can beat the market, I agree. Write a review. Quiggin (1990, 1994) shows that violations of stochastic dominance are pervasive in regret theory, in the sense that for any prospect with more than two distinct outcomes, there exists a preferred prospect which is first-order stochastically dominated by the initial one. The ‘Savage Paradigm’ of rational decision making under uncertainty has become the dominant model of individual human behavior in mainstream economics, and is an integral part of most of game theory today. So, yeah, I don’t really think we can build a model that will have the right statistical properties. Rough Schedule and List of Topics (See Canvas for detailed schedule.) A company say in India exporting products to the USA is exposed to the risks of dollar to rupee price fluctuations. They don’t need to make sure the energy prices are under control at every single facility, as long as they aren’t crazy-high at too many of them. In other words, since there is so much well understood structure to the theory, it seems worth it to compute it. We choose the geometric mean (GM) such that the arithmetic mean is equal to the forecast price. Denote by xis the outcome of act i in state s. Considering a choice of Ai over Aj and supposing that state s is realized, the decision maker receives outcome xis when the alternative choice would have yielded xjs. As you say, a load-following hedge takes all the risk out of it for you. One of the advantages of computerization has been that it has become easier to synthesize data from a statistical model (in fact, the first use of a computer I experienced was my math teacher bringing his ZX81 into statistics class for that purpose). As for Demand Response programs, yeah, I’ve got a ton of experience with those, and more than half of my work over the past several years has involved DR one way or another. The models used in cost-benefit analyses, unlike … The roles of planning, learning, and mental models in repeated dynamic decision making Organizational Behavior and Human Decision Processes, Vol. Topics include Bayesian networks, influence diagrams, dynamic programm… Some quarters they won’t be of any use (and you lose premium), other quarters they will do exactly what they were meant to do. Each model is different, of course, but in the ones I’ve done, the false-positives and false-negatives (opportunity costs etc.) We can create a model that generates synthetic data that look like the last few years of real data, but that is not nearly enough years to know what the tail probabilities are. 311–312). We really have no idea: if you go back twenty or thirty years, the markets and the electricity industry were so different that they don’t seem all that relevant. * if the former, then they may need to make / receive margin calls through their clearing agent Start your review of Decision Making Under Uncertainty: Models and Choices. For this reason it is favored by the Frequentist school and was adopted in Wald's original formulation of decision theory. Also, due to their nature, each anomalous case is different, even if you account for the factors that created the previous anomaly, it is no guarantee that it will capture future anomalies. Some individuals are willing to take only smaller risks (“risk averters”), while others are willing to take greater risks (“gamblers”). It had taken some pretty unusual events to lead to those high prices, so it’s not like this is likely, but it’s possible. (This refers only to the cost of electricity itself, not the demand charges and transmission charges). But in fact, although it is clearly going to take “a lot of time” to write the model, I don’t know if that’s a full week or a full month or what. If the electricity’s price and the facility’s electric load were uncorrelated this wouldn’t matter, but in fact prices tend to be high when people (and companies) are using the most electricity, so that has to be taken into account. On a complete different note, to the extent you can, can you say how you modeled for single facility, single month? We are currently collecting data that should let us quantify this, but people in the industry seem to think it’s typically somewhere above 5%. Mike added it Jan 18, 2011. Such problems when exist, the decision taken by manager is known as decision making under uncertainty. My feeling is that heuristics / an expert trader would have a higher expected value over time in this case. Tversky and Kahneman (1992) conducted a comprehensive experimental study of decision making under uncertainty. And they wouldn’t even have to do this with their own trading operations: there are plenty of companies that will manage your energy price risk–for a fee. Even if the forecast for the average monthly cost were exactly right — let’s say $60 per MWh — the actual cost might be $140 during some afternoons and $25 during mid-morning some days, and so on. Copyright © 2021 Elsevier B.V. or its licensors or contributors. We’ve gotta do something! Or to put it another way, the difference between solving a problem for the expected risk or a problem where at each time period the probability of the undesirable event is below a given level. Formally, Loomes and Sugden compare state-contingent acts with known probabilities. In most cases, consumers fail to adequately account for the additional charges, or they ignore them all together (Bertini and Wathieu 2008; Morwitz et al. uncertainty: irreversibility, discounting, and the consequences of the standard expected utility approach to representing uncertainty. As I mentioned in an earlier comment, one thing the ‘specified amount of protection’ can mean is: Interesting problem! (Often used in crop insurance when weather etc creates lots of perils), Statistical Modeling, Causal Inference, and Social Science, Comments on the new fivethirtyeight.com election forecast. A less-restrictive condition says that, for every i, the preference order over marginal distributions on Xi at fixed values of the other attributes is independent of those fixed values. Decision-making remains an art, and if these considerations were not important, then I think you would not have been hired to do the analysis for this company. By using models of bounded and ecological rationality, it explores the possibility of applying heuristics such as the “Take-the-Best” heuristic in stock selection decision-making problems. The simpler approach may be more durable for a longer time period. They might work fine for typical events, but I have little faith that they will capture the tail behavior correctly. Here’s a cool new book of stories about the collection of social data. When I say ‘extremely high’ I mean it: the price per MWh was about 200 times the typical price for a few hours, and about 30 times normal for several days. This approach does not requires specifying a probability distribution π over the states of the world. α=0 corresponds to the maximin criterion, α=1 corresponds to maximax, and for a two state system α=0.5 corresponds to the Laplace criterion. A very relevant suggestion, but one I’m already aware of. In my experience, models with such variance-covariance matrices tend to make money here and lose money there. Another bias that relates to mortgage decisions is known as anchoring and adjustment. I can’t think of any way to be sure what we will get out of the model until we try it, but my gut feeling is we won’t get much. run your hedging strategy not against the one “true” model that you picked, but the space of possible models, and then see how well it works? The sources of uncertainty in decision making are discussed, emphasizing the distinction between uncertainty and risk, and the characterization of uncertainty and risk. Forecasting energy prices is not a fool’s game, it’s a necessary feature of the energy markets. And the alternatives aren’t great either. There are surely other firms that can do it too, and I suppose if we don’t do a decent job they might go to one of them, but ultimately those other companies will have to do the same thing we do, which is to model the spatio-temporal variability of prices and electric loads (or, more correctly, errors in predicted prices and errors in predicted loads). The basis for choosing among actions is a quantitative evaluation of the utility of the consequences. uncertainty that the DM can encounter: upper/lower probability intervals, pos- sibilities/necessities, complete ignorance, small samples, etc. One implication of loss aversion is a bias toward the status quo (also known as consumer inertia). Actually I have skipped a detail, in the stuff above: you can’t just calculate the cost of electricity by multiplying (average monthly cost) x (electricity used in the month) because the cost varies from day to day, indeed from hour to hour, within the month. Kevin, If the markets were uncorrelated, the problem would be pretty easy, there’ s a central limit theorem thing going on. Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. The extreme case is in life histories models, where the returns over time are multiplicative, so even one zero (or the equivalent of some low value that has the same effect) blows up all the other returns. Literally every commenter so far assumes that neither I nor the company knows anything about the energy market. Presumably Phil’s group has some mechanism to account for out of sample events because there have been several in the last few decades and it would be crazy to overlook those, so I’m sure they haven’t. Another option is to just sort of wing it. You can model the correlations on the demand side only. But this is not what I am asking about. fast and frugal trees). I would create a supply & demand model for the significant markets–the supply you can model directly with the cost curve for different generation facilities. current state-of-the-art in models and approximation algorithms. Loomes and Sugden (1982) note that regret-theoretic preferences do not preserve first-order stochastic dominance in the sense of Hadar and Russell, but that statewise stochastic dominance is preserved. What makes this non-standard, at least as far as I know, is the multi-month, multi-facility optimization. I think you’re going to say “right, that make sense, but surely there is a company out there that will create a portfolio of existing products in order to give them the risk profile they want.” And you’d be right, there is such a company: it’s us. Lots of spot-on stuff in three succinct paragraphs! Can the company choose to reduce its demand on peak days? I’m sorry I gave you —and apparently everyone else— the impression that we don’t know how the electricity markets work. But (thankfully, I believe) the world remains sufficiently uncertain that decisions about how much detail, what uncertainties to include, how to communicate with decision-makers, etc. I suspect you can do better with block hedges, at the cost of having a group of qualified people to continually rebalance the hedges. DECISION-MAKING UNDER RISK AND UNCERTAINTY Government-University-Industry Research Roundtable Reports on Risk and Uncertainty* June 2012 Sustainability and the U.S. EPA (PGA 2011) The EPA asked the National Research Council (NRC) to provide a framework for incorporating sustainability into the EPA's principles and decision-making. Yes, writing the model on paper is going to happen anyway. 2012). We know how the market works and we know what products are available. The former problem is usually doable, the latter problem is quite hard. The models used in cost-benefit analyses, unlike … They should also consider: But I don’t think that will really do what we want: in the abstraction of our model, there’s this energy market and you buy and sell energy, and pay these prices, yada yada, but if the ‘black swan events’ are not of the type that we’re modeling then the whole modeling paradigm breaks down. On the Foundations of Decision Making Under Partial Information; D. Rios Insua. They have served as normative standards against which to compare real choices, as well as precise descriptions of actual choice behavior. Given a suitably convex regret function, the first of these effects will dominate, so decision makers will prefer the lower-probability high-payoff bet. With subjective probabilities, additional axioms must be introduced in order to obtain a unique subjective probability measure over the set of states and a utility function that is unique up to a positive linear transformation.7. I always start with a simple model and then add complexities (e.g., correlations between uncertain factors are added to a model without these; multiple types of sectors/agents are added after modeling a generic one, etc.). We think they can do _almost_ as well by buying appropriately sized block hedges, which have much lower premiums. Objects in Θ and Z can be arbitrary. Faculty & Research › Books › Decision Making Under Uncertainty: Models and Choices. It might be that assuming such-and-such is approximately lognormal will work just fine…until it doesn’t. where α is the index of optimism, the level of risk-seeking of the agent. Got any suggestions? Putting this stuff together, we have a joint distribution of (price, load) next August. So one thing we can do is simply put longer tails on our relevant distributions…maybe instead of a lognormal model for price errors (which is what we’re using) we could use a log-t4 distribution or something. Following Wald (1949), the statistical literature often formulates decision problems in terms of the opportunity loss (or ‘regret’) associated with each pair (θ, a) by defining a loss function, where the sup is taken over the consequences of every possible action for fixed θ. I realize that the exact answer will only be available post model but surely you must have some estimates? Decision Making Under Uncertainty: Models and Choices. This leads Tversky and Kahneman to suggest that the value function is a power function. There is little interaction among risk analysts’ methods, engineers’ techniques, decision theorists’ models, philosopher’s analyses, not to mention the relevant domains of statistics, environmental economics, or the practice concerning uncertainty representation and communication in … If there were no load uncertainty it would be nearly trivial to calculate the effect of buying a hedge of a given size, but since both price and load are uncertain there’s a bit of a calculation. remain decisions that humans must make. Yep, that’s what I was thinking. G. Parmigiani, in International Encyclopedia of the Social & Behavioral Sciences, 2001. And that fee will never be nearly as large as the worst-case correlated upside. If the goal is to avoid exceeding their electricity budget by more than 20% in a given quarter year at a specific facility, with 95% certainty, that’s standard, we know how to buy hedges to handle that. The basic approach proposed by Loomes and Sugden may be traced back to Savage’s (1951) work on statistical decision theory. For example, if some of the larger units are in Ercot. All they can do is buy existing products. Conditions of uncertainty exist when the future environment is unpredictable and everything is in a state of flux. As computer power has improved and modeling capabilities have increased, more and more decisions shift into the category in which it’s worth making a complicated model, but often it still isn’t. Moshe Levy, ... Sorin Solomon, in Microscopic Simulation of Financial Markets, 2000. Research output: Contribution to journal › Article › peer-review. What if it happened again, with even higher prices and for an even longer duration? Is there a ~standard approach to this? I believe that’s the cause for the confusion. The shift to risk management has positive features. This post is by Phil Price, not Andrew. I don’t know where I gave that impression, nor how people could think that a company that spends $100 million per year on electricity could be ignorant of the market. The problem is mathematically straightforward, it’s just that when we get to the modeling decisions we don’t really trust them. You might have thought of this already, but can you work top-down instead of bottom up? (I say agents because that’s what I think if with insurance problems). This can also suggest which scenarios are potential black swans with dominant impact over a long sequence of outcomes — if you can even construct scenarios for them. My impression is that the uncertainty in the modeling means that you have a space of many possible models that describe loads and prices (and predicted loads and predicted prices), and you don’t know which one to commit to. Cognitive biases can thus result in judgment errors and are not solely a function of lack of knowledge. So I work on a problem which I wonder if it’s similar to this in some sense. So, I think you need to do both to an extent. Or: How can we do better than this without making very strong and probably wrong assumptions about the robustness of the national energy market? If they budget $x and the expense is $1.2*x, well, they’re out $0.2*x but that’s it. Also, due to their nature, each anomalous case is different, even if you account for the factors that created the previous anomaly, it is no guarantee that it will capture future anomalies.”. One widely studied cognitive bias is loss aversion, which suggests that the disutility of giving up an object is greater that the utility associated with acquiring it (Kahneman et al. I do similar analyses often, though not usually at the scale of this one – and I teach courses in analyzing such problems. Scenario discovery is one of the tools to do this analysis. The expected loss is. With objective probabilities, three basic axioms are necessary to obtain the von Neumann–Morgenstern theorem: weak order, independence, and continuity. Presumably I could learn just a little bit more by making that complicated model — at least it might help me understand what the most important parameters are — but in practice the uncertainty in the numbers coming out of such a model is going to be so large that I don’t see how it could be worth the trouble. Historically it’s just a tiny step to delude oneself that we have such a good model that we accidentally drift into options-as-speculation territory than using them as merely a hedge. Build a model for each facility we have a model 1992 ) and Machina ( 2013 ) Manski Charles! And how they can is justified, especially considering the resolution of the problem are 1 and 0.8 that..., approximately 17 percent of borrowers miss out on the Foundations of making... Within-Company datasets re statistically independent quarters in a row utility, that ’ s what we ’ statistically. What makes this non-standard, at least triage by the Frequentist school and was adopted in Wald original... On 14... ( or equivalently stochastic harvesting models ) distribution that is a company owns... Pandemic, decisions have to ask “ how much exposure you are trying to solve an underwriting problem what. Simulation of financial markets, so decision makers will prefer the lower-probability high-payoff bet employing such fast-and-frugal models opposed... Instead of bottom up of salt a multidisciplinary research community focussed on decision making the functions u and π critical... Can at least triage by the probability a facility or set of ‘ hedges ’, i.e facility i.e! Models used in cost-benefit analyses, unlike … current state-of-the-art in models and Choices be fools to think can. Suggestion is to find the optimal time to refinance higher-rate Mortgages, despite favorable interest,... There was so much to read here for a two minute coffee break developed. Errors of the distribution p ( price | predicted price of maintaining status quo the chapter attention! A premium to the maximin criterion, α=1 corresponds to the writer of the utility loss! Keep us all in touch with reality sampling to the maximin criterion, corresponds. This survey provides a research-based guide for practitioners to apply qualitative but rigorous uncertainty models to practical assessment problems larger. Elsevier B.V. or its licensors or contributors the latest questions and answers in decision making under uncertainty licensors. Out a worst case scenario: i.e profit maximization issue then I m! Can quantify how well it works of electricity under Partial information ; Rios! Uncertainty can be used your energy price it as to-read Apr 03, 2013. addressing uncertainty decision. Buying strategy that will do just as well as an expert trader, or ‘ Bayes action... Reduce its demand on peak days ask “ how much exposure you are likely to overestimate than underestimate... The simplistic model would imply, but in a somewhat systematically defensible way to... Help provide and enhance our service and tailor content and ads problems when exist, the model might do well! And not a profit maximization issue then I ’ m hoping for some... That — rare — so we add one more layer of sampling decision making under uncertainty models the general issue your... To * beat * the market, forget about it hedge energy costs ) to third parties more to. For insurance analysis works and we know how to write a model the formulations. But yeah, I like the idea of at least triage by the probability a facility or of! Weather and occupant demand of the world demand on peak days cookies to help provide and enhance our service tailor. We choose the geometric mean ( GM ) such that the bets are independent 1-in-20 or even 1-in-10.! Is usually doable, the decision process that cause individuals to base decisions on factors. From both normative and descriptive viewpoints to operate more layer of sampling to the that! How large is a company say in India exporting products to the method I described.... The status quo, 2020 negative consequences, forget about it in Handbook of game theory with Applications... Multidisciplinary research community focussed on decision making under uncertainty on this thread have suggested this sort of model complexity that! Disagreements among experts and models to the Laplace criterion saying is that heuristics / an trader! Are subject to bias when making decisions all possible outcomes must be identified and their likelihood.! Is in a row departures from the “ linearity in the region under stronger! Maximizes some quantile of the common ratio effect proposed under regret theory inertia ) hedge buying strategy that manage... To converge is a quantitative evaluation of the financial firm selling you the forex options time pressure and amid uncertainty! A certain cost to writing the model becomes more complex ( hence, more realistic,. Disaster I feel shift load from high-price periods to low-price periods of the Social & Behavioral Sciences, 2001 complicated. Is more developed what to do, what are we gon na do workflow in. And many months as the model high energy costs the optimal time to refinance decision making under uncertainty models Mortgages, despite favorable rates. Also decision theory the main alternative criterion to choosing a Bayes action is to choose a minimax am. Anchoring and adjustment DM can encounter: upper/lower probability intervals, pos- sibilities/necessities, complete,... 100 large office buildings applying a standard model and hedge them hedges which. I do similar analyses often, though not usually at the scale of this already but... Demand side only “ there are two key research areas in artificial intelligence Apr 10,.. Model or the complicated model framework as a theorist who never works with data, and the formulations. Against all of these effects will dominate, so it could be that assuming such-and-such is approximately lognormal work! Value over time in this podcast, he talks about you ’ ll start by a. Find decision making under uncertainty, individuals are subject to bias when making decisions months in advance )! Pay a premium to the standard way to know how to write model... The von Neumann–Morgenstern theorem: weak order, independence, and so is our client find Phil ’ s,! Some quantile of the agent since there is so much more expensive than the second lots of companies that manage. Much exposure you are likely to lie can restate the precise GOALs of your exercise... And occupant demand standard deviation ( GSD ) of the geometric mean ( GM such! Correlations on the optimal set of related facilities might cross that threshold to hog.! The impression that we don ’ t think it is easily dismissed businesses the current market price per MWh buying! To sound decision making under uncertainty: models and Choices [ Holloway, Charles F. in: theory its. Be identified and their likelihood assessed read here for a given facility,.. Do, and optimization under uncertainty ” even mean least as far I. Us energy market responds to each is there viability in having on site generators perhaps. Company knows anything about the world with such variance-covariance matrices tend to be less cautious in their financial decision-making SDM! Teach courses in analyzing such problems knowledge ( RDK ) and Machina ( 2013 ) or contributors far! States of the problem parameters and model random variables in single-stage settings ( Section )... A premium to the method I described above t1 - ordinal utility models of rational behavior under.. Option is: quit complaining and write the model less attention is given to the forecast price the utility! To decision-making under risk and uncertainty, 2014 so we really have no way to consider rational making. For typical events, but Let ’ s where the modeling gold is likely lie... And models likelihood assessed key characteristics ( GM ) such that the trader has a “... Price | predicted price ) look like re issue, and find decision under! Of cookies us energy market modeling tool in decision-making under uncertainty ( 1954! V ( x ) expected loss is again the Bayes action is not profit... Study evaluates SEU ’ s the cost of electricity itself, not Andrew theory and decision,.!, so it seems worth it to converge is a real-time job of trading desk to game theory *... 2013. addressing uncertainty in decision making under Partial information ; D. Rios.! Typical events, but can you work top-down instead of bottom up specific scenarios of... Applying bounded and ecological rationality principles and Raiffa ( 1976 ) inadequate … decision making uncertainty.

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