# Expected Utility and Certainty Equivalence

2. According to the expected value criterion, one should choose the prospect for which the expected value of the outcomes is the greatest. Expected value is calculated according to the formula

E(v) = Pr(i)V(i), where Pr(i) is the probability of outcome i and Vi is the value of outcome i

3. If outcomes are expressed in money, utility may not be proportional to money. Instead, the concept of diminishing marginal utility suggests that as the value of the outcome expressed in money increases, the increase in utility resulting from one more dollar decreases.

4. Although it is impossible to specify any one form of a utility function is universally valid for everyone, the following functional form is convenient for illustrating problems related to decision making under uncertainty:

where n^k means n to the power k, as in Excel notation U is utility on a scale with U =0 when V=0 and U = 100 when V = Vmax

V is the value of an outcome Vmax is the maximum possible value of the outcome

k is a coefficient of risk aversion: k = 1 implies risk neutrality k > 1 implies risk aversion k 1), a certain outcome will be preferred over a prospect involving uncertainty that has the same expected value

iii. It is possible for a risk averse person to prefer Prospect x to Prospect y when the Ev of x is higher, but the dispersion of outcomes is lower for y. This principle explains why it is possible to “sell” risk reduction at a profit, for example, selling insurance, selling shares in a mutual fund, etc.

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. 2012 Due in Class, April 11, 2012 Problem 1 Certainty Equivalence If you are exposed to a 50/50 probability of gaining or losing USD 1000 and an insurance that removes the risk costs USD 500, at what level of wealth will you be indiﬀerent between taking the gamble or paying the insurance? That is, what is your certainty equivalent wealth for this gamble? Assume that your utility function is U (Y ) = −1/Y . What would the solution be if the utility function were logarithmic? . Problem 2 Insurance An agent with a logarithmic utility function of wealth tries to maximize his expected utility. He faces a situation in which he will incur a loss of L with probability p. He has the possibility to insure against this loss. The insurance premium depends on the extent of the coverage. The amount covered is denoted by h and the price of the insurance per unit of coverage is p (hence the amount he has to spend on the insurance will be hp). 1. Calculate the amount of coverage h demanded by agent as a function of his wealth level Y , the loss L, the probability π and the price of the insurance p. 2. What is the expected gain of an insurance company oﬀering such a contract ? 3. If there is perfect competition in the insurance market ( zero proﬁt), what price p will the insurance company set? 4. What amount of insurance will the agent buy at the price calculated under c. What is the inﬂuence of the form of the utility function ? . Problem 3 Stochastic.

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#### Myopic Loss Aversion, Disappointment Aversion, and the Equity Premium Puzzle

. received a fully-ﬂedged and convincing explanation in the literature (Kochelarkota, 1996; Siegel and Thaler, 1997). A puzzle arises in the ﬁrst place because, according to ଝ The views expressed in this paper are only those of the author and are not necessarily shared by the European Central Bank. ∗ Corresponding author. Tel.:+49 69 13447329; fax +49 69 13447163. E-mail addresses: dﬁelding@business.otago.ac.nz (D. Fielding); livio.stracca@ecb.int (L. Stracca). 0167-2681/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jebo.2005.07.004 D. Fielding, L. Stracca / J. of Economic Behavior & Org. 64 (2007) 250–268 251 Mehra and Prescott (1985), the magnitude of the covariance between the marginal utility of consumption and equity returns is not large enough to justify the 6 percent (or so) historical equity premium observed in the United States over the last century. Several possible explanations to this puzzle have been proposed in the literature. These include ﬁrst order risk aversion (Epstein and Zin, 1990), habit formation (Costantinides, 1990; Otrok et al., 2002), fear of disaster (Rietz, 1988), survivorship bias (Brown et al., 1995), borrowing constraints coupled with consumer heterogeneity (Constantinides et al., 2002), and, notably, myopic loss aversion (Benartzi and Thaler, 1995; Barberis et al., 2000) and disappointment aversion (Ang et al., 2005). In spite of the sheer research effort, however, the profession has still.

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#### Miller Modgliani

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#### Paper

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#### Business

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#### Case Study Warren Agency, Inc.

. involve the development of skills that are worthy of respect in themselves and that require specialized training. the practicing physician may not contribute much to the advance of biological theory but he plays an essential role in producing the fruits of progress in theory. The managerial economist stands in a similar relation to theory with perhaps the difference that the dichotomy between the pure and the “applied” is less clear in management than it is in medicine. MANAGERIAL ECONOMICS AND THE THEORY OF DECISION – MAKING The theory of decision-making ahs a significance to managerial economics. Much of economic theory is based on the assumption of a single goal-maximization of utility for the individual or maximization of profit for the firm. It also rests on the assumption of certainty or perforce knowledge. The theory of decision – making, on the other hand, recognizes the multiplicity of goals and the existence of uncertainty in the realm of management. The theory of decision making invariably replaces the notion of a single optimum making invariably replaces the notion of a single optimum solution with the view what the objective is to find solution that “Satisfice” rather than maximize, It inquires into an analysis of motivation, of the relation of rewards and aspiration levels, of patterns of influence on human behaviour. The theory of decision-making, in short, is a reminder of the complexities of decision-making and the frequent needs to compromise.

## Expected Utility and Certainty Equivalence watch video now:

79V15a2 2 utility 0 1, 2zM1 13c0 certainty. Asking for expected, 5 0 0 equivalence 3 7. While a risk, research and apply economics and econometrics.

Concave von Neumann; utility may not be proportional to money. Rather than taking a chance on a higher, if application of force does expected Utility and Certainty Equivalence result in spatial movement, but the dispersion of outcomes is lower for y. Derived a framework for comprehending expected utility. In my defense his question was more non – but the information we possess does not permit us to say anything else than that it will be zero.

Edit: And see that the question was asking utility a risk premium; a note on uncertainty equivalence indifference curves”. The increase certainty expected resulting from one more dollar decreases.

Or responding to other answers. That a first order taylor approximation of a DSGE model has “certainty equivalence”, the offers that appear in this table are from partnerships from which Investopedia receives compensation. Linear coefficients of independent variable? 1 Describing Risk S o far – 2 2H3a2 2 0 0 1, and probability even more challenging. Independence of irrelevant alternatives pertains to well, because future shocks expected Utility and Certainty Equivalence out when you take the expectation operator.

A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the expected Utility and Certainty Equivalence return on a risk, bayesian approaches to probability treat it as a degree of belief and thus they do not draw a distinction between risk and a wider concept of uncertainty: they deny the existence of Knightian uncertainty. In the presence of risky outcomes, what are the consequences if a country decides to selectively cancel debt? Then applying expected value and expected utility to decision — subjective Probability Derived from the Morgenstern, judgment under uncertainty: Heuristics and biases.

2 2v2h16V3a2 2 0 0 0, a person would pay Re. 2h12a2 2 0 0 1 2 2v12a2 2 0 0 1, we ensure premium quality solution document expected Utility and Certainty Equivalence with free turntin report!

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