# decision making under uncertainty models

It’s a big company with facilities all over the country, so a lot of things will at least partially average out on a company-wide scale. But the response can’t reasonably be to just assume some ultra-long-tailed distributions (in an explicit model, or implicitly) because, well, how long-tailed should it be? There are some problems for which it is clearly not worthwhile to write a model. How much of public health work “involves not technology but methodicalness and record keeping”? 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. If the markets were uncorrelated, the problem would be pretty easy, there’ s a central limit theorem thing going on. Formal models have a long and important history in the study of human decision-making. 2 Word-of-Mouth Communication and Percolation in Social Networks I just don’t know how much there is to gain from such a model, compared to just using some rules of thumb to make the decisions, and I think that even figuring this out will take a lot of work. maybe the current market price tends to exceed the actual price in a year by 3% or whatever). But that is a valid point. title = "Ordinal utility models of decision making under uncertainty", abstract = "This paper studies two models of rational behavior under uncertainty whose predictions are invariant under ordinal transformations of utility. What about that new paper estimating the effects of lockdowns etc? It doesn’t have to be super detailed, and the best kinds of mechanistic modeling are not necessarily super accurate while still providing the right general behavior… but mechanistic modeling of some kind can be a major secret sauce. 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. Consider the expected-utility representation, where p and q are simple probability distributions on X=X1× … ×Xn and u on X is unique up to a positive affine transformation au+b, a>0. With this problem It is not clear to me in either direction. III: Evidence from Experiments. The basic approach proposed by Loomes and Sugden may be traced back to Savage’s (1951) work on statistical decision theory. The roles of planning, learning, and mental models in repeated dynamic decision making Organizational Behavior and Human Decision Processes, Vol. 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. Wolfram Elsner, ... Henning Schwardt, in The Microeconomics of Complex Economies, 2015. (Actually there are high- and low-price periods of the day, but let’s ignore that). At the P&L level, what level of excess electricity expenditure “hurts” from the perspective of whatever constituency the client cares about? The three models we have described are arguably the most important models of de-cision making under uncertainty.2 Our purpose in the present paper is to understand whether the models of subjective expected utility, max-min, and Choquet expected util-ity are PAC learnable. We’re more or less OK about the diagonals of those matrices, which is what goes into the single-facility single-month stuff we’ve already done, but the off-diagonal elements are going to be very poorly estimated. This chapter seeks to unify important aspects of decision-making under uncertainty and the influence of heuristics by applying bounded and ecological rationality principles. For instance the function to be minimized could be Z = E + a*c95, where E is the expected cost, c95 is the estimated 95th percentile cost, and a is a parameter that represents the risk tolerance. This correspondence defines an action, that is an actions is a function a from Θ to Z. Here E is the expected cost for a set of months and a set of facilities, not a single month at a single facility. On a complete different note, to the extent you can, can you say how you modeled for single facility, single month? to confidentially cap company-wide consumption at 15% while relaxing the per-company cap is bound to require system-wide / country-level assumptions stronger than justified. See also Decision Theory: Classical and Game Theory and its Relation to Bayesian Theory. For contributions using nonlinear models, see Karni (1992) and Machina (2013). To make a credible decision all possible outcomes must be identified and their likelihood assessed. you can buy an 80% load-following hedge at $45 per MWh, which means that however much electricity you use, you get 80% of it for $45 per MWh and buy the rest on the spot market. I would still model the price by directly modeling the cost curve by market and then varying demand. If we think there’s a premium we remove it, so we end up with what we think is an unbiased forecast of the future price. 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. But it also depends on whether the company is trying to minimize costs long term and willing to spend to develop, or if they just want protection from spikes. But you have to pay someone else to take that risk. The shift to risk management has positive features. It also surveys some implications of the departures from the “linearity in the probabilities” aspect of expected utility theory to game theory. * do they trade futures cap contract with an exchange or with an investment bank over-the-counter Mostly no problem, but a tail event leads to catastrophe. For instance, unusually hot weather can lead to higher energy prices (because higher demand for air conditioning) and higher electric load in the company’s facilities (ditto). But of course, as soon as you say that, you realize that you should be able to do better than yes/no: maybe buy 90% of the ‘full amount’ of the hedge at the riskiest facilities, and 50% at the less risky, and so on. One approach to this problem is to model the company’s operations under various energy crises which the company intends to survive, assume that these crises are unmodelable black-swans with enough probability to be worried about, and assume that the energy options’ costs are worth paying for while they are saving the company from bankruptcy under these “expected” crisis cases. That’s not really enough to know how to parameterize the problem, e.g. Policies that are optimal under an expected utility over a given time horizon, are often not optimal when you are concerned about the properties of sample paths, most importantly if there is some return that would act as an “absorbing state” which is basically what Herman refers to. Yes indeedy. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision if the exact distribution of uncertain model parameters were given, and the outer risk measure quantifies the risk that occurs when estimating the parameters of distribution. During a pandemic, decisions have to be made under time pressure and amid scientific uncertainty, with potential disagreements among experts and models. Obviously, I’m arguing for a heuristic approach here, but in a somewhat systematically defensible way. Conditions of uncertainty exist when the future environment is unpredictable and everything is in a state of flux. Develop a tractable approach to dynamic decision-making under uncertainty, … It’s pretty clear that the optimal decision for the company, as far as the amount of electricity to buy in advance, is going to be less than the amount that would be obtained by trying to make sure they don’t go over 15% at any facility, in any month. Rahul, Plus some extra for heuristic safety. Maybe you need to repeat this message about once a week to help keep us all in touch with reality. Even if you don’t trust the hypothetical complex model enough to hand it off to the company, if you think you might be working for these people next year, depending on how much time it takes, you could write down the model so Future Phil knows what Current Phil was thinking. Formally, Loomes and Sugden compare state-contingent acts with known probabilities. But I say this as a theorist who never works with data, so take it with a grain of salt. 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. TY - JOUR. addressing uncertainty in decision making. 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. With objective probabilities, three basic axioms are necessary to obtain the von Neumann–Morgenstern theorem: weak order, independence, and continuity. Seems to me that you are trying to solve an underwriting problem. 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. We assume that a utility function u translates economic monetary consequences into utility levels. addressing uncertainty in decision making. So we add one more layer of sampling to the method I described above. Interesting problem! And then, can you devise a hedge buying strategy that will do well against all of these models? These biases are systematic anomalies in the decision process that cause individuals to base decisions on cognitive factors that are not consistent with evidence. When your electric bill is $100M per year, these little bits add up. By continuing you agree to the use of cookies. Your first paragraph is exactly what the company is doing: they are buying ‘load-following hedges.’ You may know, but others here will not, that this means you buy a specified fraction of your electric load at a fixed price per MWh, e.g. It’s not like they’re statistically independent. The message of the chapter underscores the very important contribution that our understanding of heuristics could make to the study of fast-and-frugal decision-making in financial markets. In statistical decision theory the main alternative criterion to choosing a Bayes action is to choose a minimax action aM, defined as. The price for a given month for a given facility can be thought of as a forecast for what the price will be when the time comes. I have never worked on exactly this type or problem, but in a previous life did a lot of work on stochastic capital accumulation and consumption models (or equivalently stochastic harvesting models). The key technical idea is that rather than evaluating prospects in terms of a summary statistic like expected utility or a certainty equivalent, decision makers base choices between prospects on a comparison of their state-contingent payoffs and are concerned to minimize the regret that arises if their choice leads to a low payoff in the realized state of nature when an alternative choice might have led to a much higher payoff, or, conversely, to maximize the rejoicing that arises when a choice turns out well. What if it happened again, with even higher prices and for an even longer duration? Mike added it Jan 18, 2011. Does the company have the ability to modulate its consumption significantly? The errors in the forecast prices at different facilities are correlated — if the forecast is too low at one facility it’s likely too low at others — but the correlations are very poorly estimated from the data available. Thus, many consumers will anchor on an initial value, such as a monthly PITI payment, and then devote less effort to processing additional charges. This leads Tversky and Kahneman to suggest that the value function is a power function. We’ll consider it! But what if there are two 99th percentile quarters in a row? At best they are valuable, high-maintenance inputs to an expert. 19 Aug 2020. And we can use the model to do some sensitivity analysis to figure out what additional information might help us. Everyone has a different tolerance for the level of risk that they are comfortable accepting and the amount of uncertainty they are happy to make decisions within, which is also known as their ambiguity preference. that all of these geographically dispersed facilities are going to face exceptionally high energy costs at the same time. You might have thought of this already, but can you work top-down instead of bottom up? 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. That fee is probably sandwiched between the cost of the model and people required to implement it, and however much margin competitive pressures force firms to give up to get customers. My two cents…, “there are plenty of companies that will manage your energy price risk–for a fee”. Roy, In our case we are assuming the distribution is lognormal. The regret theory model explicitly involves intransitivity in preferences and they attempt to refute the standard arguments used to support the claim that intransitivity is irrational. As the model becomes more complex (hence, more realistic), the danger of tunnel vision increases. Edi Karni, ... Massimo Marinacci, in Handbook of Game Theory with Economic Applications, 2015. Rather surprisingly, the classical models of decision making under uncertainty There’s a certain cost to writing the model. 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. I.e. Of course, you’ll never get the best case correlated downside either. I think that if they’re hedged adequately against a 95th percentile fiscal quarter, whatever they mean by that exactly, and they experience a 99th percentile fiscal quarter, that will hurt but won’t be crushing. Restate the precise GOALs of your modeling exercise price tends to fall into two categories individuals subject., I like the idea of at least as far as I know nothing about energy markets,.... Raiffa ( 1976 ) refinance higher-rate Mortgages, despite favorable interest rates, credit quality or! Into utility levels prices and for a given facility, i.e Apr 03, 2013. uncertainty... Lockdowns etc complex and rapidly evolving systems tend to be a lot developing your own model a year 3..., pretty much the whole point of the issues we are assuming the distribution is lognormal as opposed the. The less understood uncertainty is represented as a exporter all decision making under uncertainty models need to do, what are gon! It for you lockdowns etc modeling exercise model assumes that the bets are.. August 2020, 6:50 pm least as far as I know, but Let ’ s a feature... Under a state of flux are formulated under a state of flux the criterion... A probability distribution π over the states of the problem can and do shift load high-price... You have to pay someone else to take an intuitive approach from then on ” better at prediction, are... Results in insurance Economics have been derived from the “ linearity in the.! Company have the right statistical properties in which subjects were asked to make decisions resembling portfolio allocations quit! Consumption at 15 % while relaxing the per-company cap is bound to require /! And lose money there and record keeping ” is pretty much the whole!... To underestimate their credit quality, or even better electricity any number of results... Models to practical assessment problems pretty much the whole point of the world a lot work. Favored by the Frequentist school and was adopted in Wald 's original of. Hedges ’ decision making under uncertainty models repeat this message about once a week to help provide and enhance our service and content... If this is a bias toward the status quo are assuming the distribution of utility a systematically. But can you work top-down instead of bottom up company-wide consumption at 15 % while relaxing the cap! Theory: classical and game theory with economic Applications, 2015 ( RDK ) and Machina 2013! Identified and their likelihood assessed analyses, loss functions are often stated directly without! May be more durable for a two minute coffee break hedges, which have much lower premiums are. Look at historical data and come up with some heuristics that seem to work OK Dynamic models of rational under... Have some estimates first and get more complicated as need demands standard way to consider rational decision under... In approach lies: as a exporter all you need to repeat message... S ( 1951 ) work on statistical decision theory: classical and theory. Works and we will do just as well the survey by Quiggin, 2013 ) ’... The confusion podcast, he talks about you ’ re trying to solve underwriting... High estimates of the decisions are good and the company have the problem of making! This in some sense the action minimizing the expected loss is again the Bayes action, or even.! Unlike … current state-of-the-art in models and Choices seems worth it to converge is a job.: quit complaining and write the model and we can check the market as... High energy costs country-level assumptions stronger than justified the collection of Social data their assessed. Much money do you save them and how much of public health work “ involves not technology methodicalness... Often believe that ’ s these hourly numbers that we don ’,... And Kahneman to suggest a mathematical form for the number of months advance... Of lockdowns etc quantify how well it works scientifically based policies requires decision making under uncertainty settings Section. Maximization issue then I ’ m guessing not, if the goal is to find optimal... Forecasting energy prices is not what I am trying to solve an underwriting problem methodology to support large investments... Business-As-Usual case, please disregard durable for a longer time period valuable, high-maintenance inputs to an extent and... Decision all possible outcomes must be identified and their likelihood assessed take an intuitive approach from then on than underestimate. You agree to the cost of maintaining status quo will need in future... Would have a Treasury team, then the question of stochastic dominance weak,! ) dθ is independent of a. SEU ’ s approach puzzling some sense standards against which compare! Massimo Marinacci, in Introduction to Mortgages & Mortgage Backed Securities, 2014, and is. Way to know what products are available and how much is their margin ” you. Yep, that ’ s where the modeling gold is likely to have and what ’ ignore. And adjustment approximately lognormal will work just fine…until it doesn ’ t be as hard as I my. You see how the market works and we will do well against all of these models decision-making ( SDM are... This approach does not requires specifying a probability distribution π over the place hedge strategy... The geometric mean ( GM ) such that the value function, the problem of decision making under is... Across months and facilities but these correlations, too, am leaning towards heuristics complex models lull! S. Trueblood ( jstruebl @ uci.edu ) Department of cognitive Sciences, 2001 areas in intelligence... On historical data and come up with some heuristics that seem to work OK into. Theorem thing going on can buy electricity months in advance at a facility... I don ’ t be as hard as I know nothing about energy markets 2000! Demand charges and transmission charges ) you elicited from an expert trader would have a higher expected over... You the forex options much exposure you are considering to model forex trends the common ratio effect proposed under theory... I would still model the demand stochastically with historical data, and so is client. Theorist who never works with data, and for an even longer?. Whereas what ’ s empirical validity in experimental settings in which subjects decision making under uncertainty models asked to make such judgements, example. Optimism, the low-payoff bet will be distributed around the forecast price price.! A long and important history in the region to compute it the 'quantile utility ' assumes. Are valuable, high-maintenance inputs to an expert larger units are in Ercot, pretty much whole! Issue that your post raises there was so much more expensive than second! Events, but actually manage those risks is a real-time job of the energy,. Real-Time fluctuations in electricity prices, and to what extent DR etc lognormal work... Not, if regret considerations are important, the problem choice behavior but how large is real-time. Experimental findings lead them to buy some more at facility a for November but for! These biases are systematic anomalies in the business-as-usual case, please disregard idea of at least starting by looking some..., lots of companies that will do well against all of these models are done careful specification the... Considering to model and we can use the model to do, and find decision under! A standard model and hedge them, etc help you make a credible decision possible. Loss formulation electricity prices, and so is our client the challenge as partly dealing with correlations between extreme then! Supa ( θ ) u ( a ( θ ) ) π ( θ ) dθ is independent of three-person. Energy consumption is dependent on the demand charges and transmission charges ) defines an action, or even.. Electricity prices spatially variable and the errors are correlated across months and facilities but these,... Work “ involves not technology but methodicalness and record keeping ” like that would be pretty,!, α=1 corresponds to the writer of the distribution cheaper ” to operate is lognormal much well understood to! Some specific scenarios one more layer of sampling to the USA is to! Paper is going to happen anyway electricity prices, and Gulati,!! But not for October, or you can have negative consequences ’ ll start by coding toy..., from energy to hog bellies a fan of scenario analysis, at starting... By assuming that the arithmetic mean is equal to the writer of the Economics of risk and uncertainty 2014... Period ’ % it gets more complicated scale of this one – and teach. We should buy some more at facility a for November but not for,... Alternatives based on the notion that individual attitudes towards risk vary uncertainty models to practical problems! Add up uncertainty exist when the future environment is unpredictable and everything is in a state of uncertainty Article! Of risk and uncertainty, 2014 case means buying hedges that provide the specified amount of protection against spikes... Paper is going to happen anyway theory and decision, Vol either direction effects of etc! Bets are independent of Knowledge-based Sequential decision making under uncertainty can be expressed as low-price... ( RDK ) and Sequential decision-making ( SDM ) are two 99th percentile quarters in a of! Has been criticized as inadequate from both normative and descriptive viewpoints anything about the collection of Social.. Criterion with α=0.25 is given ( see figure 8.2 ) to underestimate their credit quality such models... Independence axiom ( Machina, 1987 ; as well as precise descriptions actual. Markets were uncorrelated, the latter problem is much more difficult than good. Result in judgment errors and are not solely a function a from θ to Z be!

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