Draft: Coherent Risk Measures
... than VaR. The reader should carefully read the proof given in that section. Especially for distributions that are not continuous there are slight corrections needed in order to have coherent risk measures. We do not discuss more severe measures of risk, although we could have given examples that sho ...
... than VaR. The reader should carefully read the proof given in that section. Especially for distributions that are not continuous there are slight corrections needed in order to have coherent risk measures. We do not discuss more severe measures of risk, although we could have given examples that sho ...
Risk-Averse Strategies for Security Games with
... for two canines to patrol Terminals 1, 2, 3, 4 with probabilities of 0.2, 0.8, 0.5, 0.5 respectively. However, a last-minute cargo inspection may require a canine unit to be called away from, say, Terminal 2 in its particular patrol, or an extra canine unit may become available by chance and get sen ...
... for two canines to patrol Terminals 1, 2, 3, 4 with probabilities of 0.2, 0.8, 0.5, 0.5 respectively. However, a last-minute cargo inspection may require a canine unit to be called away from, say, Terminal 2 in its particular patrol, or an extra canine unit may become available by chance and get sen ...
FINITE ADDITIVITY VERSUS COUNTABLE ADDITIVITY
... space have a probability, and for each set this may be calculated by summing over the probabilities of the singleton sets of the points it contains. (This is of course in the countably additive case; in the finitely additive case, one can have all finite sets of zero probability, but total mass 1.) I ...
... space have a probability, and for each set this may be calculated by summing over the probabilities of the singleton sets of the points it contains. (This is of course in the countably additive case; in the finitely additive case, one can have all finite sets of zero probability, but total mass 1.) I ...
local pdf - University of Oxford
... origin may be traced back to the famous 4:15 PM report at JP Morgan, where an early application of VaR was presented. Although VaR is a popular tool for risk measurement in practice, it has been noted that VaR has some defects. Artzner et al. [1] introduced the class of coherent risk measures, which ...
... origin may be traced back to the famous 4:15 PM report at JP Morgan, where an early application of VaR was presented. Although VaR is a popular tool for risk measurement in practice, it has been noted that VaR has some defects. Artzner et al. [1] introduced the class of coherent risk measures, which ...
Desirable Properties of an Ideal Risk Measure in Portfolio Theory
... that investors minimize the probability of the investment return falling below a specified risk benchmark. In particular, even if there are no apparent connections between the expected utility approach and a more appealing benchmark-based approach, expected utility can be reinterpreted in terms of t ...
... that investors minimize the probability of the investment return falling below a specified risk benchmark. In particular, even if there are no apparent connections between the expected utility approach and a more appealing benchmark-based approach, expected utility can be reinterpreted in terms of t ...
How bad is a 10% chance of losing a toe?
... scales represented expected disutility. Thus, although we should expect both of these scales to be monotonically related to EU, we should not expect them to be linearly related. Each response scale could be some transform of EU. Thus, we transformed the variables for each subject so that the transfo ...
... scales represented expected disutility. Thus, although we should expect both of these scales to be monotonically related to EU, we should not expect them to be linearly related. Each response scale could be some transform of EU. Thus, we transformed the variables for each subject so that the transfo ...
Slides - Rutgers Statistics
... It is curious that this axiomatization is restrictive on the range of all probability functions: the real numbers in [0,1], and not a richer set; yet it is almost completely permissive about their domains: can be any set you like, however large, and F can be any field on , however large. ...
... It is curious that this axiomatization is restrictive on the range of all probability functions: the real numbers in [0,1], and not a richer set; yet it is almost completely permissive about their domains: can be any set you like, however large, and F can be any field on , however large. ...
u t c o r R esearch e p o r t
... V1 (ω) ≤ V2 (ω) holds for all ω ∈ Ω. The extended real line is denoted by = ∪ {−∞, +∞}. For a value x ∈ we denote the Dirac delta measure concentrated on x by δx . Throughout our paper larger values of random variables are considered to be preferable. In this context, risk measures are often referre ...
... V1 (ω) ≤ V2 (ω) holds for all ω ∈ Ω. The extended real line is denoted by = ∪ {−∞, +∞}. For a value x ∈ we denote the Dirac delta measure concentrated on x by δx . Throughout our paper larger values of random variables are considered to be preferable. In this context, risk measures are often referre ...
Theory of Decision under Uncertainty
... uncertainty. After teaching such classes for many years, it became more difficult to squeeze all the material into class discussions, and I was not quite sure about the appropriate order in which the issues should be presented. Trying to put everything in writing, and thereby finding at least one perm ...
... uncertainty. After teaching such classes for many years, it became more difficult to squeeze all the material into class discussions, and I was not quite sure about the appropriate order in which the issues should be presented. Trying to put everything in writing, and thereby finding at least one perm ...
NBER WORKING PAPER SERIES INTERPRETING PREDICTION MARKET PRICES AS PROBABILITIES Justin Wolfers
... Fourth, while only log utility yields an exactly linear demand function, almost all of these functions are approximately linear over the range in which beliefs are within about 10-20 percentage points of the price. This suggests that for distributions of beliefs that are not too disperse, market pri ...
... Fourth, while only log utility yields an exactly linear demand function, almost all of these functions are approximately linear over the range in which beliefs are within about 10-20 percentage points of the price. This suggests that for distributions of beliefs that are not too disperse, market pri ...
On The Quantitative Definition of Risk
... of risk, the next section addresses the precise meaning adopted in this paper for the term “probability.” In particular, at this point, we carefully draw a distinction between “probability” and “frequency.” Then, using this distinction, we return to the idea of risk, and give a “second-level” defini ...
... of risk, the next section addresses the precise meaning adopted in this paper for the term “probability.” In particular, at this point, we carefully draw a distinction between “probability” and “frequency.” Then, using this distinction, we return to the idea of risk, and give a “second-level” defini ...
Interpreting Prediction Market Prices as Probabilities
... Fourth, while only log utility yields an exactly linear demand function, almost all of these functions are approximately linear over the range in which beliefs are within about 10-20 percentage points of the price. This suggests that for distributions of beliefs that are not too disperse, market pri ...
... Fourth, while only log utility yields an exactly linear demand function, almost all of these functions are approximately linear over the range in which beliefs are within about 10-20 percentage points of the price. This suggests that for distributions of beliefs that are not too disperse, market pri ...
Probability metrics applied to problems in portfolio theory
... The development of the theory of probability metrics started with the investigation of problems related to limit theorems in probability theory. The limit theorems have a very important place in probability theory, statistics, and all their applications. A well-known example is the celebrated Centra ...
... The development of the theory of probability metrics started with the investigation of problems related to limit theorems in probability theory. The limit theorems have a very important place in probability theory, statistics, and all their applications. A well-known example is the celebrated Centra ...
Probability metrics with applications in finance
... The development of the theory of probability metrics started with the investigation of problems related to limit theorems in probability theory. The limit theorems have a very important place in probability theory, statistics, and all their applications. A well-known example is the celebrated Centra ...
... The development of the theory of probability metrics started with the investigation of problems related to limit theorems in probability theory. The limit theorems have a very important place in probability theory, statistics, and all their applications. A well-known example is the celebrated Centra ...
46656 Varieties of Bayesians (#765)
... physical probabilities corresponding to the cells o f multidimensional contingency tables. Many cells will be empty for say a 2'' table. A Bayesian proposal for this problem was made in Good (p. #75 o f #398), and I am hoping t o get a student to look into it; and to compare i t with the use o f log ...
... physical probabilities corresponding to the cells o f multidimensional contingency tables. Many cells will be empty for say a 2'' table. A Bayesian proposal for this problem was made in Good (p. #75 o f #398), and I am hoping t o get a student to look into it; and to compare i t with the use o f log ...
Sensitivity, Specificity, and Useful Measures of Diagnostic Utility
... in medicine. The receiver of a diagnostic measurement . . . wants to make a decision based on some xc , and is not especially interested in how well he would have done had he used some different cutoff. ...
... in medicine. The receiver of a diagnostic measurement . . . wants to make a decision based on some xc , and is not especially interested in how well he would have done had he used some different cutoff. ...
Learning and Risk Aversion"
... attitudes of expected utility maximizers. Our analysis, hence, provides a bridge between decision theory and learning theory.3 In contrast to decision theory in which the agent selects an (optimal) action based on her beliefs about the distributions over payo¤s of each action, a learning rule speci… ...
... attitudes of expected utility maximizers. Our analysis, hence, provides a bridge between decision theory and learning theory.3 In contrast to decision theory in which the agent selects an (optimal) action based on her beliefs about the distributions over payo¤s of each action, a learning rule speci… ...
Subjective multi-prior probability: A representation of a partial
... Savage (1954), and others who followed in their footsteps, introduced conditions on a binary relation over events that characterize when it may be represented by a prior probability. However, situations in which some events are incomparable cannot be captured by a single prior probability, as a sing ...
... Savage (1954), and others who followed in their footsteps, introduced conditions on a binary relation over events that characterize when it may be represented by a prior probability. However, situations in which some events are incomparable cannot be captured by a single prior probability, as a sing ...
The Axioms of Subjective Probability
... rise against the dollar next year means roughlythat you would ratherbet on the first-namedevent fora valuable prize that you will receive if your chosen event obtains. Comparativeprobabilityaxioms are usuallythought of as criteriaof consistencyand coherencefora person's attitudes toward uncertainty. ...
... rise against the dollar next year means roughlythat you would ratherbet on the first-namedevent fora valuable prize that you will receive if your chosen event obtains. Comparativeprobabilityaxioms are usuallythought of as criteriaof consistencyand coherencefora person's attitudes toward uncertainty. ...
Document
... color and 3 are of another color? P(3 one color, 2 another) = s s+f = (2 colors from 4)(2 same from 7)(3 same from 7) total possible = (4 nPr 2)(7 nCr 2)(7 nCr 3)/(28 nCr 5) ≈ 0.0897 ≈ 9% ...
... color and 3 are of another color? P(3 one color, 2 another) = s s+f = (2 colors from 4)(2 same from 7)(3 same from 7) total possible = (4 nPr 2)(7 nCr 2)(7 nCr 3)/(28 nCr 5) ≈ 0.0897 ≈ 9% ...
MODEL UNCERTAINTY
... of beliefs about models.14 Yet for decision problems this distinction is questionable at an ontological level because, as mentioned previously, all uncertainty that is relevant to decision problems is, ultimately, epistemic (i.e., relative to the state of DMs’ information). In this paper we regard p ...
... of beliefs about models.14 Yet for decision problems this distinction is questionable at an ontological level because, as mentioned previously, all uncertainty that is relevant to decision problems is, ultimately, epistemic (i.e., relative to the state of DMs’ information). In this paper we regard p ...
The Enigma Of Probability - Center for Cognition and Neuroethics
... you might get for increasing amounts of money is today called an utility curve. If the utility, as described by a suitable utility curve, is inserted instead of the actual amounts of money you could win in the St. Petersburg game, the expected value, or rather the expected utility, becomes finite. T ...
... you might get for increasing amounts of money is today called an utility curve. If the utility, as described by a suitable utility curve, is inserted instead of the actual amounts of money you could win in the St. Petersburg game, the expected value, or rather the expected utility, becomes finite. T ...
Utility Issues with CSST Gas Piping
... Bonding Conductor Sizing Conductor at least 6 AWG copper or 4 AWG aluminum Conductor single or multi-strand Conductor length and gauge are inter-related, but length is not specified in the NEC ...
... Bonding Conductor Sizing Conductor at least 6 AWG copper or 4 AWG aluminum Conductor single or multi-strand Conductor length and gauge are inter-related, but length is not specified in the NEC ...
Uncertain Decisions and The Many Minds
... we use (B) to guide our actions. For we only use (B) when we know the single-case probabilities. And when we know the single-case probabilities (B) is a special case of (C): for example, if you know the single-case probability is 0.8, then you know that H happens in 80% of cases-like-the-situation-y ...
... we use (B) to guide our actions. For we only use (B) when we know the single-case probabilities. And when we know the single-case probabilities (B) is a special case of (C): for example, if you know the single-case probability is 0.8, then you know that H happens in 80% of cases-like-the-situation-y ...
Estimating Subjective Probabilities
... Subjective probabilities about some event are operationally defined as those probabilities that lead an agent to make certain choices over outcomes that depend on that event. These choices could be as natural as placing a bet on a horse race, or as structured as responding to the payoffs provided b ...
... Subjective probabilities about some event are operationally defined as those probabilities that lead an agent to make certain choices over outcomes that depend on that event. These choices could be as natural as placing a bet on a horse race, or as structured as responding to the payoffs provided b ...