Question: Let X be exponential, and u(x) = e x . Show that the certainty equivalent c(X) 0 as . Interpret it in terms of

Let X be exponential, and u(x) = −e−βx. Show that the certainty equivalent c(X) → 0 as β→∞. Interpret it in terms of risk aversion.

Step by Step Solution

★★★★★

3.48 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

From M182 it follows that cX 1 In E eBX nEex If X is exponential with parameter a t... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Probability And Stochastic Modeling Questions!

Q:

The Equity Premium Puzzle: Investments in equities (like stocks) yield substantially higher returns than investment in bonds. By itself, this is no surprisebecause stocks are riskier than bonds. What...

Q:

Let X be exponential with expected value 3. Let Y be another random variable that depends on X as follows: if X > 5, then Y = X - 5; otherwise, Y = 0. a. Find the expected value of Y. b. Find the...

Q:

Find d (e*ee") ex+e (1+ e") ex+ e* (e* + 1) ee*+1(e *+(ee* + 1) O ex(ee" + 1)

Q:

Consider an investor with an initial wealth of $5 with the following utility function: s x for 55 U(x) = for x > 5 (a) Draw a sketch of the utility function U(x) labelling the main features. (b)...

Q:

Consider an investor with an initial wealth of $5 with the following utility function: for x 5 (a) Draw a sketch of the utility function U(x) labelling the main features. (b) Classify an investor...

Q:

Consider an investor with an initial wealth of $5 with the following utility function: Szx for 55 U(X) = 22 for 5 10 (a) Draw a sketch of the utility function U(x) labelling the main features. (b)...

Q:

(1.1) An individual has the following utility function: u (w) = w /2. Her initial wealth is 10 and she faces the lottery X : (-6, 7: +6, ;). (a) Compute the exact value of the certainty equivalent...

Q:

(10 marks) Consider an investor with an initial wealth of $5 with the following utility function: for x 5 (a) Draw a sketch of the utility function U(@) labelling the main features. (b) Classify an...

Q:

Distribute one disjunction from the formula over a conjunction or fail if no such disjunction exists: A (B C) ' (A B) (A C) [6 marks] (iv) Repeatedly apply the distribution step until no more...

Q:

MEAN 6.0000 WHEN WE HAVE LARGE DATA SETS, WE GROUP THE DATA. IN THIS CASE OUR GROUPS WILL BE: STD DEV 2.17 IN A NORMAL DISTRIBUTION THE MEAN, MEDIAN AND MODE ARE ALL THE SAME NUMBER X-VALUES Z-VALUES...

Q:

What is the purpose for establishing pay ranges?

Q:

The South African Airways (SAA) briefed the Committee on its Long-Term Turnaround Strategy (LTTS), which was implemented in April 2013 in order to address the challenges that SAA had been...

Q:

Stock Y has a beta of 0 . 7 and an expected return of 8 . 2 6 percent. Stock Z has a beta of 1 . 9 and an expected return of 1 5 . 0 8 percent. What would the risk - free rate ( in percent ) have to...

Q:

? provides medical care, rehabilitation, and lost wages for injured workers as well as death benefits for the dependents of persons killed in work-related accidents. a. unemployment insurance c....

Q:

Consider a Markov chain with states 0, 1, 2, ... and such that P+ p. 1 P- - where po 1. Find the necessary and sufficient condition on the p,'s for this chain to be positive recurrent, and compute...

Q:

Compute the expected number of plays, starting in i, in the gambler's ruin problem, until the gambler reaches either 0 or N.

Q:

In the gambler's ruin problem show that P{she wins the next gamble present fortune is i, she eventually reaches N} [p[1-(q/p) [1-(q/p)'] =(i + 1)/2i if p if p =

Q:

Quad Enterprises is considering a new three-year expansion project that requires an initial fixed asset investment of $2.37 million. The fixed asset will be depreciated straight-line over its...

Q:

Daisy Company received a bank statement for February, as follows: Date Checks Deposits Balance Feb. 1 $ 4,524.80 7 $ 2,700.33 $8,642.61 9 3,484.81 14 6.00 SC 460.00 CM 16 274.09 21 4,133.60 3,385.49...

Q:

3. Interpreting a simplified balance sheet As Aa Consider this table, which shows hypothetical balance-of-payments data for the United States. Choose the correct value for each of the boxes....