Suppose an insurance buyer has initial wealth Wo, uses as utility function u(w)=-e^(-w) and faces a risk X. The distribution of X is determined by some probability density function f(x). The insurance buyer wants to determine the maximal premium he/she is willing to pay to get rid of the risk X based on the expected utility. Calculate if X~exp(2), i.e. f(x)=2e^(-2x) for x>=0. How can the minimum premium an insurer will ask for insurance be calculated? Under what condition an insurance contract is possible?

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