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However, in this case the value at risk becomes equivalent to a mean-variance approach where the risk of a portfolio is measured by the variance of the portfolio's return. The Wang transform function (distortion function) for the Value at Risk is g ( x ) = 1 x ≥ 1 − α {\displaystyle g(x)=\mathbf {1} _{x\geq 1-\alpha }} .
A risk measure is defined as a mapping from a set of random variables to the real numbers. This set of random variables represents portfolio returns. The common notation for a risk measure associated with a random variable X {\displaystyle X} is ρ ( X ) {\displaystyle \rho (X)} .
A dynamic risk measure is a risk measure that deals with the question of how evaluations of risk at different times are related. It can be interpreted as a sequence of conditional risk measures. [1] A different approach to dynamic risk measurement has been suggested by Novak. [2]
Risk is the lack of certainty about the outcome of making a particular choice. Statistically, the level of downside risk can be calculated as the product of the probability that harm occurs (e.g., that an accident happens) multiplied by the severity of that harm (i.e., the average amount of harm or more conservatively the maximum credible amount of harm).
Under some conditions, aggregate risk can arise from the aggregation of micro shocks to individual agents. This can be the case in models with many agents and strategic complementarities; [5] situations with such characteristics include: innovation, search and trading, production in the presence of input complementarities, and information ...
In machine learning, specifically empirical risk minimization, MSE may refer to the empirical risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The MSE is a measure of the quality of an estimator.
The term 'risk transfer' is often used in place of risk-sharing in the mistaken belief that you can transfer a risk to a third party through insurance or outsourcing. In practice, if the insurance company or contractor go bankrupt or end up in court, the original risk is likely to still revert to the first party.
However, in practice it would be difficult to use since quantifying the risk aversion for an individual is difficult to do. The entropic risk measure is the prime example of a convex risk measure which is not coherent. [1] Given the connection to utility functions, it can be used in utility maximization problems.