Question

3.7 An insurance company is looking to replace its legacy claims payment system. The Technology Steering Committee is willing to explore three alternative systems. Table EX 3.7 summarizes the cost savings for each system under potential peak claims volumes. Table EX 3.7 Payoff: Cost Savings (in $000s) for Peak ClaIMS: see table below a. The most recent system implementation was riddled with data conversion issues and end-user resistance. Accordingly, members of the Technology Steering Committee are relatively pessimistic decision makers. Which system would be selected under a Hurwitz value of 0.2? b. Which system would be selected under minimax regret? c. Which system would be selected using the Laplace strategy solution? d. The company's information technology (IT) department submitted a proposal to develop an in-house solution for claims payment. This in-house solution is expected to provide cost savings of $25,000 for five million claims, $75,000 for ten million claims, and $120,000 for fifteen million claims. Determine if the system selection changes in parts (a) through (c) when the in-house system is added as an alternative.

Payoff: Cost Savings (in $000s) for Peak Claims Volumes System

System 5,000,000 CLAIMS 10,000,000 CLAIMS 15,000,000 CLAIMS A

A 35 70 105

B (50) 85 170

C 10 25 75

Answer 1

a) b) c)

A 35 70 2 System 3 A 4 B 5 C 5,000,000 Claims 10,000,000 Claims 15,000,000 Claims Min payoff Hurwicz payoff Laplace payoff 105 170 -50 -6 68.33333333 75 10 23 36.66666667 -50 10 25 6 7 Regret table 8 System 5,000,000 Claims 10,000,000 Claims 15,000,000 Claims max regret 9 A 10 B 85 085 11 C 95 95 12 13 Decision criteria Selected Payoff Decision 14 Pessimistic 35 A 15 Hurwicz 49 A 16 Laplace 17 Minimax regret 65 A 18 70 A

Formula

5,000,000 Claims 10,000,000 Claims 2 System 3 A 4 B 5 C 15,000,000 Claims 105 170 Min payoff =MIN(B3:03) =MIN(B4:04) =MIN(B5:05) Hurwicz payoff =0.2*MAX(B3:D3)+(1-0.2) *MIN(B3:D3) =0.2*MAX(B4:04)+(1-0.2) *MIN(B4:04) =0.2*MAX(B5:05)+(1-0.2) *MIN(B5:05) Laplace payoff -AVERAGE(B3:D3) =AVERAGE(B4:04) -AVERAGE(B5:05) -50 85 10 35 75 5,000,000 Claims 10,000,000 Claims =MAX($B$3:$B$5)-B3 =MAX($C$3:$C$5)-C3 =MAX($B$3:$B$5) -B4 =MAX($C$3:$C$5)-C4 =MAX($B$3:$B$5)-B5 =MAX($C$3:$C$5)-C5 15,000,000 Claims =MAX(D$3:D$5)-D3 =MAX(D$3:D$5)-D4 =MAX(D$3:D$5)-D5 max regret =MAX(B9:09) =MAX(B10:010) =MAX(B11:011) 7 Regret table 8 System 9 A 10 B 11 C 12 13 Decision criteria 14 Pessimistic 15 Hurwicz 16 Laplace 17 Minimax regret 18 Decision Selected Payoff =MAX(E3:E5) =MAX(F3:F5) =MAX(G3:65) MIN(E9:E11) 20

d)

With the in-house option,

F G H -50 Laplace payoff 49 -6 68.33333333 23 36.66666667 44 73.33333333 85 2 System 5,000,000 Claims 10,000,000 Claims 15,000,000 Claims Min payoff Hurwicz payoff 3 A 105 4 B -50 85 170 5 C 10 75 10 6 In-house 120 25 7 Regret table 8 System 5,000,000 Claims 10,000,000 Claims 15,000,000 Claims max regret 9A 65 10 B 0 0 85 11 C 25 60 95 12 In-house 10 50 13 Decision criteria Selected Payoff Decision 14 Pessimistic 35 A 15 Hurwicz 49 A 16 Laplace 73.33333333 In-house 17 Minimax regret 50 In-house 18 19 10 20

Formula

ДА 5,000,000 Claims 10,000,000 Claims 15,000,000 Claims 105 85 170 -50 10 Min payoff =MIN(B3:D3) =MIN(B4:04) =MIN(B5:05) =MIN(B6:06) Hurwicz payoff Laplace payoff =0.2*MAX(B3:D3)+(1-0.2) *MIN(B3:D3) -AVERAGE(B3:D3) =0.2*MAX(B4:04)+(1-0.2)*MIN(B4:04) =AVERAGE(B4:04) =0.2*MAX(B5:05)+(1-0.2)*MIN(B5:05) -AVERAGE(B5:05) =0.2*MAX(B6:06)+(1-0.2)*MIN(B6:06) =AVERAGE(B6:06) 120 2 System 3 A 4 B 5 C 6 In-house 7 Regret table 8 System 9A 10 B 11 C 12 In-house 13 Decision criteria 14 Pessimistic 15 Hurwicz 16 Laplace 17 Minimax regret 10,000,000 Claims =MAX($C$3:$C$6)-C3 =MAX($C$3:$C$6)-C4 =MAX($C$3:$C$6)-C5 =MAX($C$3:$C$6)-C6 Decision 15,000,000 Claims =MAX(D$3:D$6) -D3 =MAX(D$3:D$6)-D4 =MAX(D$3:D$6)-D5 =MAX(D$3:D$6)-D6 5,000,000 Claims =MAX($B$3:$B$6)-B3 =MAX($B$3:$B$6)-B4 =MAX($B$3:$B$6)-B5 =MAX($B$3:$B$6)-B6 Selected Payoff =MAX(E3:56) =MAX(F3:F6) =MAX(G3:46) =MIN(E9:E12) max regret =MAX(B9:09) =MAX(B10:010) =MAX(B11:011) =MAX(B12:012) In-house In-house 19

As seen. decision changes to In-house for Laplace and Minimax regret criteria