You are attempting to establish the utility that your boss assigns to a payoff of $1,200. You have established that the utility for a payoffof $0 is zero and the utility for a payoff of $10,000 is one. Your boss has just told you that they would be indifferent between a payoffof $1,200 and a lottery which has a payoff of $10,000 where the probability of losing is 0.9. What is your boss' utility for $1,200?(Round your answer to 1 decimal place.)Utility of $1,200< Prev2 of 5Next >

To find out? The utility function of $1200

Answered: You are attempting to establish the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 70P

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A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet 1. From then on, every time you win a bet, you bet 1 the next time. Each time you lose, you double your previous bet. Currently you have 63. Assuming you have unlimited credit, so that you can bet more money than you have, use simulation to estimate the profit or loss you will have after playing the game 50 times.
In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?
You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
You have 5 and your opponent has 10. You flip a fair coin and if heads comes up, your opponent pays you 1. If tails comes up, you pay your opponent 1. The game is finished when one player has all the money or after 100 tosses, whichever comes first. Use simulation to estimate the probability that you end up with all the money and the probability that neither of you goes broke in 100 tosses.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
Based on Marcus (1990). The Balboa mutual fund has beaten the Standard and Poors 500 during 11 of the last 13 years. People use this as an argument that you can beat the market. Here is another way to look at it that shows that Balboas beating the market 11 out of 13 times is not unusual. Consider 50 mutual funds, each of which has a 50% chance of beating the market during a given year. Use simulation to estimate the probability that over a 13-year period the best of the 50 mutual funds will beat the market for at least 11 out of 13 years. This probability turns out to exceed 40%, which means that the best mutual fund beating the market 11 out of 13 years is not an unusual occurrence after all.
You are attempting to establish the utility that your boss assigns to a payoff of $1,000. You have established that the utility for a payoff of $0 is zero and the utility for a payoff of $10,000 is one. Your boss has just told you that they would be indifferent between a payoff of $1,000 and a lottery which has a payoff of $10,000 where the probability of losing is 0.7. What is your boss' utility for $1,000? (Round your answer to 1 decimal place.) Utility of $1,000
If a $900,000 30-year fully amortizing fixed rate mortgage loan from City National Bank has an annual interest rate of 6.25% with a monthly payment of $5,541.45, and a $900,000 15-year fully amortizing fixed rate mortgage loan from Wells Fargo Bank has an annual interest rate of 5.25% with a monthly payment of $7,234.90, a borrower should: a. Choose the 30-year fixed rate loan from City National Bank because of the lower monthly payments b. Make a careful analysis of all the terms and conditions of the available loans to determine which loan is better for that borrower under the circumstances, or if another loan or lender should be considered c. Choose a 7-year adjustable rate interest-only loan from PNC Bank instead with a low teaser interest rate of 1.0% for the first loan year d.Choose the 15-year fixed rate loan from Wells Fargo because of the lower interest rate

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