Quantitative Risk Management - Assignment Example

Decision Analysis Name Professor Course Date Decision Analysis a) In case of a theft, how much would Danika have to pay; (i) Under the NoRegrets package The NoRegrets package is a comprehensive premium and caters for everything in case of theft. Therefore Danika will not be required to pay up any amount in case the office goods are stolen. (ii) The InsureNow package The InsureNow package requires Danika to pay an amount of $5000 in case the office goods are stolen. After the $1500 premium amount has been paid out, she will not pay any amount more than the stipulated figure. (iii) The RiskIt package The RiskIt package offers up to 75% cover to the insured goods in case of robbery. The projected figure of the office goods is $15000 therefore Danika will be required to pay 25% amounting to a figure of $3750. Therefore in case the office is broken into, she will be required to pay $3750. (a) Construct a payoff table that models Danika’s problem, and determine the optimal choice under the (i) maximin, (ii) maximax, (iii) maximum likelihood and (iv) expected value criterion. 1. Maxi-max Criterion: This is an optimist point of view (criterion) where a decision made will result in the realization of maximum of maximum payoffs i. For every action choose max. profit. ii. Choose the action which has the max. of these max. profits. PAY-OFF TABLE-1 STATUS OF NATURE ALTERNATIVES Not Stolen Stolen NoRegrets $2000 $0 InsureNow $1500 $5000 RiskIt $1000 $3750 Answer: Max-max Action = Go, Optimal Plan = $2000 For NoRegrets Max payoff is $ For RiskIt Max payoff is $ Maximum of the above mentioned maximum values is $2000 so choice is NoRegrets 2. Maximum likelihood Criterion This is the pessimists view criterion as he always expects the worst. The judgment of the decision maker therefore works this way: i. For each action choose min. profit. ii. Choose the action which has the max. of these min. profits. PAY-OFF TABLE-2 STATUS OF NATURE ALTERNATIVES Not Stolen Stolen NoRegrets $2000 $0 InsureNow $1500 $5000 RiskIt $1000 $3750 Answer: Max-max Action = Go, Optimal Plan = $2000 For Max payoff is $1000 For max payoff is $0 Minimum of these above mentioned maximum values is $0 so choice is Stop decision 3. Maxi-min Criterion: In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion. i. For each action choose min. profit. ii. Choose the action which has the max. of these min .profits. PAY-OFF TABLE-3 STATUS OF NATURE ALTERNATIVES Not Stolen Stolen NoRegrets $2000 $0 InsureNow $1500 $5000 RiskIt $1000 $3750 Answer: Max-max Action = $0 For RiskIt Min payoff is $1000 For NoRegrets min payoff is $0 Maximum of these above mentioned maximum values is $0 so choice is RiskIt Rakina believes that there is a .05 probability that thieves will break into the office and steal office equipments. Therefore using the Baye’s Criterion we calculate the EMV (Expected Monetary Value) for each action as follows: PAY-OFF TABLES-4 EVENTS OR STATES OF NATURE ALTERNATIVES Not Stolen Stolen A1 = No Regret $2000 $0 A2= RiskIt $1000 $3750 Prior Probs. .95 .05 EMV = 2000*.95 + 0*.05 = 1900 EMV RiskIt stop = 1000 *.95 + * .05 = 0 Hence, according to Baye’s Criterion: Optimal Act = A2, EMV* = $ 0 c. Which package would you choose? Justify your answer. The best choice to consider is the RiskIt package. That package is best suited for a risk-neutral insurance buyer as the payoff table 4 has suggested. Although the uncertainities exist, this analysis used the prior probabilities to come up with the decision. There are 0.05 chances of thieves breaking into the office and therefore risking $1000 for a probability of 0.95 is a better package. The individual understands the prior probabilities through past statistics and therefore is more comfortable gambling for that package. References McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative risk Management: Concepts, Techniques and Tools. Princeton university press. Read More