Calculate the maximum premium that Jayne would be prepared to pay to insure herself against the total loss of her house worth 100,000 if her initial level of wealth was 140,000 and comment on your results. You may assume that Jayne's utility function can be described as U (w) = w and that the probability of a loss of 100,000 is 0.01. (ii) Suppose that UN Life plc has an initial wealth of 100 million and a utility function of the form U(w)=w. Find the minimum premium UN Life plc would require in order to offer insurance to Jayne and comment on whether insurance is feasible in this instance. Use a general reasoning argument to construct Thiele's differential equation for a regular premium n-year term assurance for a life aged x by considering the change in reserves over a short time period. Assume that: interest is earned continuously at force of interest 8; premiums are payable continuously at rate Ppa; and the sum assured of 1 is payable immediately on death.