Certainty Equivalent

4 Key excerpts on "Certainty Equivalent"

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  Encyclopedia of Medical Decision Making

  • Michael W. Kattan(Author)
  • 2009(Publication Date)
  • SAGE Publications, Inc

    (Publisher)

  Taken into consideration by the individual is the degree to which any of these outcomes may be certain. That is, although the benefit derived from an event with a lesser or unknown likelihood of occurring may be much greater, people often tend to opt for the less advantageous, although more certain, outcome. An influential variable, however, is to what degree the individual finds the certain outcome to be of value. Thus, Certainty Equivalents are the amount of util-ity, or usefulness, that a person will consider to forgo an offered gamble. When the person becomes indifferent between the choice of a certain event and a probabilistic one, the value of the certain event is called the Certainty Equivalent . Certainty Equivalents are used most frequently in an outward sense within the realm of economic ventures, though individuals may subconsciously use the framework for any scenario in which a gamble presents itself. The utility terms will there-fore vary with the application as what is consid-ered beneficial is highly circumstantial. Within medical decision making, however, certainty equiv-alents could include financial aspects relating to choices in care, various measures of quality of life for the self and for others, or potential recovery periods. The difference between the expected value of indefinite outcomes and the Certainty Equivalent is referred to as the risk premium. Finding Certainty Equivalents A number of mathematical methods exist for find-ing the Certainty Equivalent based on the utility func-tion being presented. However, in practice, a person’s Certainty Equivalent can be found more pragmati-cally by asking a series of questions. Each question should ask the person to choose one of two options. The first option presents a gamble, whereas the sec-ond option presents a certain outcome. If the person chooses the gamble, a second question is posed. This time, the first option remains the same, but the con-ditions of the gamble are altered.

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  Decision Theory

  Principles and Approaches

  • Giovanni Parmigiani, Lurdes Inoue(Authors)
  • 2009(Publication Date)
  • Wiley

    (Publisher)

  We are now ready to explore in more detail how utility functions for money typically look. Say you are about to ship home a valuable rug you just bought in Samarkand for $9000. The probability that it will be lost during transport is 3% according to your intelligence in Uzbekistan. At which price would you be indifferent between buying the insurance or taking the risk? This price defines your Certainty Equivalent of the lottery defined by shipping without insurance. Formally, assume that the outcome space Z is an open interval, that is Z = ( z 0 , z 0 ) ⊆ . Then, using the same notation as in Chapter 3, a Certainty Equivalent is any reward z ∈ that makes you indifferent between that reward for sure, or choosing action a . Definition 4.1 (Certainty Equivalent) A Certainty Equivalent of lottery a is any amount z ∗ such that χ z ∗ ∼ a , (4.2) or equivalently, u ( z ∗ ) = z u ( z ) p ( z ). (4.3) A Certainty Equivalent is also referred to as “cash equivalent” and “selling price” (or “asking price”) of a lottery. 4.2.2 Risk aversion Meanwhile, in Samarkand, you calculate the expected monetary loss from the unin-sured shipment, that is $9000 times 0.03 or $270. Would you be willing to pay more to buy insurance? If you do, you qualify as a risk-averse individual. If you define ¯ z = z zp ( z ) (4.4) as the expected reward under lottery a , then: Definition 4.2 (Risk aversion) A decision maker is strictly risk averse if χ ¯ z a . (4.5) 58 DECISION THEORY: PRINCIPLES AND APPROACHES Someone holding the reverse preference is called strictly risk seeking while someone who is indifferent is called risk neutral . It turns out that the definition above is equivalent to saying that the decision maker is risk averse if χ ¯ z χ z ∗ ; that is, if he or she prefers the expected reward for sure to receiving for sure a Certainty Equivalent.

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  Handbook of the Economics of Risk and Uncertainty

  • Mark Machina, W. Kip Viscusi(Authors)
  • 2013(Publication Date)
  • North Holland

    (Publisher)

  Cummings and Laury divided up the bags of cash prior to the flight to Miami, where screenings and detentions could be triggered by high cash amounts in carry-on bags. Charles A. Holt and Susan K. Laury 150 hypothetical had little or no effect on overall decision patterns. Models with increasing relative risk aversion will be considered in Section 4.7 . 4.2.4 Price Based Assessments of a Certainty Equivalent In addition to the investment method (a single choice among a structured set of alterna-tive portfolios) and the choice menu method (structured binary choices), there is a third approach to risk elicitation that is based on finding a subject’s Certainty Equivalent money value of a gamble. Harrison (1986) first used the Becker et al. (1964) method to determine Certainty Equivalents for a set of gambles with a range of “win” probabilities associated with the high payoff outcome. This “BDM” method was structured so that subjects were asked to provide a “selling price” for a gamble. Then a “buying price” would be randomly generated. If the buying price is above the subject’s selling price, then the subject receives a money amount equal to the buying price; otherwise the subject retains the gamble, which is played out to determine the earnings. Since the amount received from a sale is not the posted selling price, it is a dominant strategy for subjects to post selling prices that equal their certainty-equivalent money values for the gamble. To see the intuition, think of a descending price auction in which the proposed selling price is lowered continuously until a bid is obtained, and the seller would receive an amount of money for the gamble that is equal to that bid. Thus a seller should “stay active” unless the proposed selling price falls below their own “keep value,” so the exit point reveals the seller’s value.

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  Benefit-cost Analysis

  A Political Economy Approach

  • A. Allan Schmid(Author)
  • 2019(Publication Date)
  • Taylor & Francis

    (Publisher)

  2 is the Certainty Equivalent of the uncertain expected value and can be used to adjust project benefits.

  Figure 10.2 Gambler's Indifference Maps

  It is conceivable that experience might confirm a number of points such as A and B in Figure 10.2 . For example, there is a two-stage drawing in the Irish Sweepstakes. The winners are assigned a horse in the sweepstakes race. These horses' chances of winning have probabilities attached to them by experts and the betting of others. The payoffs to the order of finish are given. Enterprising and relatively risk-neutral bookies then offer the holders of the tickets a choice between a certain amount of money for their ticket or the uncertain chance of a higher payoff. Willingness to accept these offers could be observed. This might give a clue to analysts in deciding the shape of alternative indifference maps to be presented to decision makers for their choice. Even so, it stretches credulity to imagine politicians making meaningful choices by these maps. There is a problem in going from the magnitude of choices faced by the average person and the millions at stake in a public project. Some simple transformation is not easily justified. Still, perhaps this line of inquiry deserves more thought.

  10.2.6. Relevance of Risk in Public Decisions

  Benefit-cost analysis requires data on the Certainty Equivalent of an uncertain project result. If people differ in their subjective probabilities, they will not agree on the appropriate Certainty Equivalent or risk premium. But if there were perfect and complete markets for all possible contingent claims, people could adjust their portfolios so that risk aversion for all would be equated at the margin. Such complete and costless markets are highly unlikely (Brainard and Dolbear 1971). This means that public choice is necessary among the conflicting views of risk assessment.

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