The entrepreneur's risk exposure in terms of annual losses is as below Probability of loss Severity...

 

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The entrepreneur's risk exposure in terms of annual losses is as below Probability of loss Severity of 0,01 400 The insurer makes a bid to compensate losses at the annual premium of 12. The non-insured losses are not tax exempt. The tax rate is 20%. Under the Expected Utility model, decide whether the entrepreneur will accept the bid, if he a. is risk neutral b. exhibits the constant risk aversion with the parameter a-0,003. risk aversion tax rate premium 0,80 0,15 0,04 {Hint: adjust losses to taxation rules : f.ex. loss of 100 needs pre-tax income of 125 to set of it Remember that utility function tells apart gains (positive numbers) and losses/expanses (negative numbers). In (b) the utility function 1-exp(-alfa outcome) has a positive exponent for losses or expenses. Prob. of loss 0,8 0,15 0,04 0,01 Exp. uninsured loss (a) Utility of prermium (a) Exp. uninsured loss (b) Utility of prermium (b) 0.003 0,2 12 loss 0 10 100 Severity if Utility of Loss severity uninsured loss 0 10 100 400 0 12,5 -0,038212 125 -0,4549914 500 -3,4816891 -11,875 -12 -0,0587483 -0.0366558 (a) will not buy insurance since the expected loss from the lottery is better than a sure expense of 12, i.e. 11,875<12 (b) will buy insurance since the utility of paid premium 1-exp(0,03*12)=-0,0367 is higher than the expected utility of the lottery-0, 05875) The entrepreneur's risk exposure in terms of annual losses is as below Probability of loss Severity of 0,01 400 The insurer makes a bid to compensate losses at the annual premium of 12. The non-insured losses are not tax exempt. The tax rate is 20%. Under the Expected Utility model, decide whether the entrepreneur will accept the bid, if he a. is risk neutral b. exhibits the constant risk aversion with the parameter a-0,003. risk aversion tax rate premium 0,80 0,15 0,04 {Hint: adjust losses to taxation rules : f.ex. loss of 100 needs pre-tax income of 125 to set of it Remember that utility function tells apart gains (positive numbers) and losses/expanses (negative numbers). In (b) the utility function 1-exp(-alfa outcome) has a positive exponent for losses or expenses. Prob. of loss 0,8 0,15 0,04 0,01 Exp. uninsured loss (a) Utility of prermium (a) Exp. uninsured loss (b) Utility of prermium (b) 0.003 0,2 12 loss 0 10 100 Severity if Utility of Loss severity uninsured loss 0 10 100 400 0 12,5 -0,038212 125 -0,4549914 500 -3,4816891 -11,875 -12 -0,0587483 -0.0366558 (a) will not buy insurance since the expected loss from the lottery is better than a sure expense of 12, i.e. 11,875<12 (b) will buy insurance since the utility of paid premium 1-exp(0,03*12)=-0,0367 is higher than the expected utility of the lottery-0, 05875)

Answer rating: 100% (QA)

The question youre asking pertains to decisionmaking under uncertainty and requires calculating the expected utility of two scenarios to determine whether the entrepreneur will accept the insurance bi... View the full answer