E
Edwin
Member
Hi all,
Just to share with those who believe in rigour. Convexity of a risk measure is a simple Mathematical property called Jensen's Inequality i.e the Expectation of averages is greater than the function of averages.
Or E[F(X)]>F[E(X)]
Also;-
f(t(x1)+(1-t)f(x2)) <= tf(x1)+(1-t)f(x2)
This explains;-
1) Subadditivity of risk measures
2) Aggregation of risks
3) The reason why solvency II works or even why ERM works
4) Also applies to portfolio risk management, say why 20% cash verses 80% Derivatives is better than Exchange Traded Funds.
SEE BELOW;-
PS;- There is nothing special about Mathematics as a cognitive domain.
Just to share with those who believe in rigour. Convexity of a risk measure is a simple Mathematical property called Jensen's Inequality i.e the Expectation of averages is greater than the function of averages.
Or E[F(X)]>F[E(X)]
Also;-
f(t(x1)+(1-t)f(x2)) <= tf(x1)+(1-t)f(x2)
This explains;-
1) Subadditivity of risk measures
2) Aggregation of risks
3) The reason why solvency II works or even why ERM works
4) Also applies to portfolio risk management, say why 20% cash verses 80% Derivatives is better than Exchange Traded Funds.
SEE BELOW;-
PS;- There is nothing special about Mathematics as a cognitive domain.
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