Question: Problem 1Assume an individual has the following utility function:u(w)=w2Her initial wealth is10 and she faces the lottery tilde(x):(-6,12;+6,12).Compute the exact value of the certainty equivalent

Problem 1Assume an individual has the following utility function:u(w)=w2Her initial wealth is10 and she faces the lottery tilde(x):(-6,12;+6,12).Compute the exact value of the certainty equivalent and of the risk premium.What is the mathematical expectation of this gamble?Problem 2What is the approximation of the risk premium? Use Arrow-Pratt approach to answer thisquestion. Explain the difference between the approximated risk premium and its exact value youcomputed in Problem 1. What is this investor's risk aversion ratio?Problem 3How will certainty equivalent and risk premium change if the utility function becomes (the samegamble faced by another investor):u(w)=w4Explain the differences in results you obtained in Problem 1, Problem 2 and Problem 3. Interpretthe differences between risk aversion ratios of the two investors.

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