2. Warren is risk-averse, with Bernoulli utility function u(w) = Vw and initial wealth W.He has access to an investment opportunity described by the following lottery: finalwealth 4W with probability 1/2, final wealth W/9 with probability 1/2. Treat W as agiven number.(a) What is the expected wealth generate by the lottery?(b) What is Warren's expected utility for this lottery?(c) What is Warren's certainty equivalent of this lottery?(d) What is the difference (meaning subtraction) between the lottery's expectedwealth and the certainty equivalent?

It is given that Warren has access to an investment opportunity described as follows:-Final wealth…

Answered: 2. Warren is risk-averse, with…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.4: Expected Value

Problem 1E: If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the...

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If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the expected value of this game is E=0.9+0.1= .
(b) A milk man buys milk at K10 per litre and sells it at K12 if sold on the same day; if not, it can be sold at K9 per litre the next day. Demand of milk lies between 45 litres and 60 litres per day and its probabilities are uniformly distributed over this demand. If each day’s demand is independent of the previous day’s demand, how many litres should be ordered every day?
Mike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the load
Consider two assets (X and Y) with mX = 10%, mY = 10%, σX2=.16, σY2=.25, and Cov(X,Y) = -.125. What is the expected return and variance of the portfolio having 70% invested in X and 30% invested in Y? Compare the risk and return of this portfolio with the risks and returns associated with investing everything in either X or Y. a) What is p(XY)? b) What is the expected return of the portfolio (m.7X+.3Y)? c) What is the standard deviation of the portfolio (s.7X+.3Y)? d) How does the standard deviation of the portfolio (s.7X+.3Y) compare to the standard deviations of assets X and Y? Show all work and formulas used in EXCEL
6 Suppose there are two periods, O and 1. Denote Stochastic discount factor by m(51), where s1 is a random state, 51€ S and Expectation under physical probabilities by E. Denote the payoff of an asset in each state by (s1). Select all (possibly multiple) claims which are true. Select one or more: O a. Discount factor = E{m(s1)] O b. The price of the asset at period O = E(v(51)m(s+)] O c. Atomic (Arrow securities) prices are equal to the stochastic discount factor for each state times the probability of each state. O d. Risk neutral probability is equal to the stochastic discount factor for each state times the probability of each state divided by E[m(s1)]. O e. The stochastic discount can be negative (for standard instantaneous utility we considered)
There are two investments projects A and B each involving an initial investment of $2,000. The possible payoffs of investments A are $1,000, $2,000 and $3,000 with respective probabilities 0.20, 0.40, and 0.40, while the possible payoffs of investment B are $1,600, $2,000, and $2,750 with respective probabilities 0.25, 0.35, and 0.40. Calculate the expected value and the standard deviation of the payoff for each of the two investments.
Explain the nature of and the difficulties caused by each of the following: a. Heteroscedasticity b. Autocorrelated errors
You and two other people are to place bids for an object, with the high bid winning. If you win, you plan to sell the object immediately for 10,000.(a) How much should you bid to maximize your expected profit if you believe that the bids of the others can be regarded as being independent and uniformly distributed between 7,000 and 10,000?
Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million production facility. The decision tree is shown in Figure 4.16. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $59 million.…
4.) Consider an M/M/2 system with an arrival rate of 9 per minute and a service rate of 8 per minute. What is the probability a newly arriving customer will have to wait? Take your answer to three decimal places.
If the moment generating function of a random variable X is: (1/3+(2/3)e t ) 5 find P (X > 3).
Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 9 8 Medium complex, d2 13 3 Large complex, d3 19 -9 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $16 million and as long as the payoff for the weak demand was greater…

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