Exercise 2

An agent faces the risk of losing all their initial wealth, equal to R euros, with a probability of p. Their Von Neumann-Morgenstern utility function is given by u(w) = log(1 + w), where w represents the agenti's final wealth. The agent can subscribe to an insurance policy by paying a premium of for each insured euro. This means that they must pay the amount A to receive the amount A from the insurance company if the damage occurs.

1. Determine the optimal insurance choice A*.

2. In which case does the agent choose to fully insure themselves(A* = R)?