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# risk CONCEPT Unreviewed

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 âexpected valueâ) 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, ânow we increase the risk,â 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 (âupsideâ 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 âmoment-basedâ 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.

Definition contributed by Anonymous

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