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However if we held a portfolio that consisted of 50% of each bond by value then the 95% VaR is 35% (= 0.5*0.7 + 0.5*0) since the probability of at least one of the bonds defaulting is 7.84% (= 1 - 0.96*0.96) which exceeds 5%. This violates the sub-additivity property showing that VaR is not a coherent risk measure.
However, a finitely additive set function might not have the additivity property for a union of an infinite number of sets. A σ-additive set function is a function that has the additivity property even for countably infinite many sets, that is, μ ( ⋃ n = 1 ∞ A n ) = ∑ n = 1 ∞ μ ( A n ) . {\textstyle \mu \left(\bigcup _{n=1}^{\infty ...
Intuitively, the additivity property says that the probability assigned to the union of two disjoint (mutually exclusive) events by the measure should be the sum of the probabilities of the events; for example, the value assigned to the outcome "1 or 2" in a throw of a dice should be the sum of the values assigned to the outcomes "1" and "2".
The use of money as compensation can often turn real cases like these into situations where the weak additivity condition is satisfied even if the values are not exactly additive. The value of a type of goods, e.g. chairs, dependent on having some of those goods already is called the marginal utility.
Coombs' theory in all three studies was applied to a set of six statements. These authors found that the axioms were satisfied, however, these were applications biased towards a positive result. With six stimuli, the probability of an interstimulus midpoint order satisfying the double cancellation axioms at random is .5874 (Michell, 1994).
How does my credit score affect my loan chances? Hanneh Bareham. February 27, 2024 at 6:01 PM. Key takeaways. ... How your credit score affects your chance of getting a personal loan.
In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions.
With some personal loan rates as high as 35.99 percent APR, the cost of the loan might be more than your potential investment return. In addition, there will be fewer lenders who will likely be ...