tie4203-20-tut-06.pdf - TIE4203 Decision Analysis in Industrial Operations Management Tutorial#6 Question 1(P6.1 For each of the following utility

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TIE4203 (2020) tut-06-1 TIE4203 Decision Analysis in Industrial & Operations Management Tutorial #6 Question 1 (P6.1) For each of the following utility functions, determine its risk tolerance and degree of absolute risk aversion. ( a ) The quadratic utility function: u ( w ) = w β w 2 ( b ) The logarithmic utility function: u ( w ) = ln w ( c ) The power utility function: u ( w ) = sgn( β ) w β Note: > = < = 0 if 1 0 if 0 0 if 1 ) sgn( x x x x Question 2 (P6.2) John has the utility function u ( x ) = 1 – 3 - x /50 over the range of x = –\$50 to \$5000. ( a ) What is John’s risk attitude? ( b ) What is John’s degree of absolute risk aversion? ( c ) At what probability ( p ) of winning \$50 versus losing \$50 with (1 – p ) probability is John indifferent between having this deal and not having this deal? Question 3 (P6.3) Jim follows the delta property and owns two independent deals L 1 and L 2 , where a , b , c , and d are prospects in dollars. Let L 3 be the following compound deal: Show that the certainty equivalent of L 3 is the sum of the certain equivalents of L 1 and L 2 . a b p 1 -p L 1 ~ c d q 1 - q L 2 ~ p L 3 ~ a + c a + d q 1 - q b + c b + d q 1 - q 1 -p
TIE4203 (2020) tut-06-2 Question 4 (P6.4)