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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).
A simple risk matrix is often used to transform these inputs into a level of risk, generally expressed as unacceptable, marginal or acceptable. If unacceptable, measures must be taken to reduce the risk to an acceptable level, and the outcome of the risk assessment must be accepted by the affected parties before a dive commences.
when the two marginal functions and the copula density function are known, then the joint probability density function between the two random variables can be calculated, or; when the two marginal functions and the joint probability density function between the two random variables are known, then the copula density function can be calculated.
LOPA is a risk assessment undertaken on a 'one cause–one consequence' pair. The steps of a LOPA risk assessment are: [4] Identify the consequences, using a risk matrix; Define the risk tolerance criteria (RTC), based on the tolerable/intolerable regions on the risk matrix; Define the relevant accident scenario, e.g. mechanical or human failure
The marginal probability P(H = Hit) is the sum 0.572 along the H = Hit row of this joint distribution table, as this is the probability of being hit when the lights are red OR yellow OR green. Similarly, the marginal probability that P(H = Not Hit) is the sum along the H = Not Hit row.
The covariance matrix can be used to compute portfolio variance. RiskMetrics assumes that the market is driven by risk factors with observable covariance. The risk factors are represented by time series of prices or levels of stocks, currencies, commodities, and interest rates.
The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 × 2 contingency table. In principle, any number of rows and columns may be used. There may also be more than two variables, but higher order contingency tables are difficult to represent visually.
Risk aversion implies that their utility functions are concave and show diminishing marginal wealth utility. The risk attitude is directly related to the curvature of the utility function: risk neutral individuals have linear utility functions, while risk seeking individuals have convex utility functions and risk averse individuals have concave ...