# Define absolute risk tolerance to be the inverse of the ArrowPratt measure of absolute risk aversion

## Description

1.5 Prove that dRA(z)/dz > 0 implies that da/dWo < 0 ‘tWo and dRA(z)/dz = 0 implies that da/dWo = 0 ‘tWo in the context of Section 1.21.

1.7 Define absolute risk tolerance to be the inverse of the ArrowPratt measure of absolute risk aversion. Show that solutions to (1.27.1) and (1.27.2) all exhibit linear absolute risk tolerance.

1.8 Fix an individual with an increasing and strictly concave utility function u and consider the gamble of (1.17.1). Define the insurance premium z to be the maximum amount of money the individual is willing to pa)’ to avoid the gamble. That is, z is the solution to the following

u(Wo – z) = pu(Wo + ht) + (1 – p)u(Wo + h2).

Obviously, z depends upoil the initial wealth, W0 , and we will denote this dependence by z(Wo). Show that, when the risk is small,

dRA(z)/dz < 0 ‘Vz if dz(Wo)/dWo < 0v Wo;

1.9. Show that utility functions of (1.27.2) imply two fund monetary

separation .

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