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# risk CONCEPT

Formally and mathematically speaking, the minimal definition of risk is what (Rothschild and Stiglitz, 1970) call a mean-preserving increase in dispersion. A typical example is a gamble offering \$400 or \$600 based on the outcome of a coin flip (i.e. with equal probability (50%)); this is less risky as compared to a similar gamble offering \$200 or \$800 [again depending on the outcome of a coin flip]. Notice here that the mean outcome (or “expected value”) remains the same for both gambles.

Thus risk can increase by keeping both the probabilities and the expected value the same.

There are other approaches to risk that are less mathematically stringent but have higher ecological validity. For instance increasing the probability of a (positive outcome) is associated with a reduced perception of risk. Notice though now that the expected value (or the mean outcome) also increases. So, it is difficult in that case to disentangle the two metrics.

Many times the term risk is associated with the probability of a negative outcome, or what is formally called downside risk. This idea is mostly due to the way actuarial science and insurance companies (which are more interested in the negative aspects of risk) use the term. For instance, the statement, “now we increase the risk,” might be translated as taking more perilous actions, but formally, this is not the case. The point of risk is that the opportunity also increases (“upside” risk). Thus, a situation that is riskier can be attractive, especially if the agent focuses on the positive outcomes.

Another approach is the so-called “moment-based” approach. Here, one is interested in the second or higher moments of a distribution, roughly corresponding to variance, skewness and kurtosis. Skewness is of particular interest because it seems that risk-seeking persons (gamblers) can be attracted by positively skewed outcomes. Bets that offer a small probability of a high outcome are attractive to gamblers (Garrett and Sobel, 1999).

Overall, risk is not a unitary concept and should be very carefully defined.

Note that the term risk as used here should be distinguished from the way the term is used in sentences such as "risk of developing Parkinson's disease". An epidemiologist could help on the definition in that context.

Input by other contributors:
the probability or likelihood that an event will occur; possibility of loss or injury; someone or something that creates or suggests a hazard; the chance that an investment will lose value.

## Asserted relationships to other concepts

 no associations are kinds of risk is a kind of no associations no associations are parts of is a part of
 riskis a kind of No associations riskis a part of decision making kinds ofrisk No associations parts ofrisk No associations

## Tasks that are asserted to measure risk

 pumps parametric (details)
 probability of highest reward (details)

## User Discussion

"definition updated from APA dictionary of Psychology 1st ed."

## Term History

REVISION 8

Definition contributed by GChristopoulos about one year ago:Formally and mathematically speaking, the minimal but also more “clean” definition of risk is what (Rothschild and Stiglitz, 1970) call a mean-preserving increase in dispersion. A typical example is a gamble offering \$400 or \$600 based on the outcome of a coin flip (i.e. with equal probability (50%)) is less risky as compared to a similar gamble offering \$200 or \$800 [again depending on the outcome of a coin flip]. Notice here that the mean outcome (or “expected value”) remains the same for both gambles. Thus risk can increase by keeping both the probabilities and the expected value the same. There are other approaches to risk that are less mathematically stringent but have higher ecological validity. For instance increasing the probability of a (positive outcome) is associated with a reduced perception of risk. Notice though now that the expected value (or the mean outcome) also increases. So, it is difficult in that case to disentangle the two metrics. Many times the term risk is associated with the probability of a negative outcome, or what is formally called downside risk. This idea is mostly due to the way actuarial science and insurance companies (which are more interested in the negative aspects of risk) use the term. For instance, the statement, “now we increase the risk,” might be translated as taking more perilous actions, but formally, this is not the case. The point of risk is that the opportunity also increases (“upside” risk). Thus, a situation that is riskier can be attractive, especially if one focuses on the positive outcomes. Another approach is the so-called “moment-based” approach. Here, one is interested in the second or higher moments of a distribution, roughly corresponding to variance, skewness and kurtosis. Skewness is of particular interest because it seems that risk-seeking persons (gamblers) can be attracted by positively skewed outcomes. Bets that offer a small probability of a high outcome are attracti

REVISION 7

Definition contributed by GChristopoulos about one year ago:Formally and mathematically speaking, the minimal but also more “clean” definition of risk is what (Rothschild and Stiglitz, 1970) call a mean-preserving increase in dispersion. A typical example is a gamble offering \$400 or \$600 based on the outcome of a coin flip (i.e. with equal probability (50%)) is less risky as compared to a similar gamble offering \$200 or \$800 [again depending on the outcome of a coin flip]. Notice here that the mean outcome (or “expected value”) remains the same for both gambles. Thus risk can increase by keeping both the probabilities and the expected value the same. There are other approaches to risk that are less mathematically stringent but have higher ecological validity. For instance increasing the probability of a (positive outcome) is associated with a reduced perception of risk. Notice though now that the expected value (or the mean outcome) also increases. So, it is difficult in that case to disentangle the two metrics. Many times the term risk is associated with the probability of a negative outcome, or what is formally called downside risk. This idea is mostly due to the way actuarial science and insurance companies (which are more interested in the negative aspects of risk) use the term. For instance, the statement, “now we increase the risk,” might be translated as taking more perilous actions, but formally, this is not the case. The point of risk is that the opportunity also increases (“upside” risk). Thus, a situation that is riskier can be attractive, especially if one focuses on the positive outcomes. Another approach is the so-called “moment-based” approach. Here, one is interested in the second or higher moments of a distribution, roughly corresponding to variance, skewness and kurtosis. Skewness is of particular interest because it seems that risk-seeking persons (gamblers) can be attracted by positively skewed outcomes. Bets that offer a small probability of a high outcome are attracti

REVISION 6

Definition contributed by GChristopoulos about one year ago:Formally and mathematically speaking, the minimal but also more “clean” definition of risk is what (Rothschild and Stiglitz, 1970) call a mean-preserving increase in dispersion. A typical example is a gamble offering \$400 or \$600 based on the outcome of a coin flip (i.e. with equal probability (50%)) is less risky as compared to a similar gamble offering \$200 or \$800 [again depending on the outcome of a coin flip]. Notice here that the mean outcome (or “expected value”) remains the same for both gambles Thus risk can increase by keeping both the probabilities and the expected value the same. There are other approaches to risk that are less mathematically stringent but have higher ecological validity. For instance increasing the probability of a (positive outcome) is associated with a reduced perception of risk. Notice though now that the expected value (or the mean outcome) also increases. So, it is difficult in that case to disentangle the two metrics. Many times the term risk is associated with the probability of a negative outcome, or what is formally called downside risk. This idea is mostly due to the way actuarial science and insurance companies (which are more interested in the negative aspects of risk) use the term. For instance, the statement, “now we increase the risk,” might be translated as taking more perilous actions, but formally, this is not the case. The point of risk is that the opportunity also increases (“upside” risk). Thus, a situation that is riskier can be attractive, especially if one focuses on the positive outcomes. Another approach is the so-called “moment-based” approach. Here, one is interested in the second or higher moments of a distribution, roughly corresponding to variance, skewness and kurtosis. Skewness is of particular interest because it seems that risk-seeking persons (gamblers) can be attracted by positively skewed outcomes. Bets that offer a small probability of a high outcome are attractive to gam

REVISION 5

Definition contributed by RPoldrack about five years ago:the probability or likelihood that an event will occur; possibility of loss or injury; someone or something that creates or suggests a hazard; the chance that an investment will lose value.

REVISION 4

Definition contributed by ABakkour about six years ago:the probability or likelihood that an event will occur; possibility of loss or injury; someone or something that creates or suggests a hazard; the chance that an investment will lose value.

REVISION 3

Definition contributed by BGregory about six years ago:possibility of loss or injury; someone or something that creates or suggests a hazard; the chance that an investment will lose value.

REVISION 2

Definition contributed by BGregory about seven years ago:possibility of loss or injury; someone or something that creates or suggests a hazard; the chance that an investment will lose value. (from merriam-webster.com)

REVISION 1

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