HW2-sln.pdf - SEEM4480 Decision Methodology and...

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SEEM4480 Decision Methodology and ApplicationsAssignment 2 Solution1.(a) The degree of risk aversion isr(w) =-u′′(w)u(w)=1w10,000It is a decreasing function in w, hence the Decision maker is lessrisk-averse when he/she has more wealth w.(b)u(CE(l)) = 0.9×ln(250,000-10,000)+0.1×ln(100,000-10,000) =12.29CE(l) = 227,577.69Insurance premium = 250,000-227,557.69 = 22,422.31Expected Monetary Value =0.9×250,000+0.1×100,000 = 235,000Fair premium = 250,000-235,000 = 15,000Risk premium = 22422.31-15000 = 7,422.31(c) Risk premium = Insurance premium - Fair premium2.(a)π(Do not drill)=0.14;π(Keep all)=.20×.350+.10×.520+.07×.835+.03×1.000 = 0.21045;π(Sell 1/2)=.60×.040+.20×.305+.10×.435+.07×.740+.03×.950 =0.2088;π(Sell 1/4)=.60×.075+.20×.255+.10×.350+.07×.600+.03×.835 =0.19805;π(Sell 3/4)=.60×.110+.20×.202+.10×.255+.07×.395+.03×.600 =0.17755;The wildcatter should choose to drill and keep all.(b) The Decision tree is drawn in the following figure 1.3.(a) The decision tree is in Figure 2(b) The strategy should be (1) do the review (2) If it is predicted suc-cessful, then to publish, otherwise not publish.4. Take the derivative ofp1(w1) + (1-p1)u(w2) =kwith respect tow1,yields

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