My Math Forum  

Go Back   My Math Forum > Science Forums > Economics

Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance


Reply
 
LinkBack Thread Tools Display Modes
October 22nd, 2015, 05:44 PM   #1
Newbie
 
Joined: Oct 2015
From: Cambridge United Kingdom

Posts: 1
Thanks: 0

Risk aversion, certainty equivalence, stochastic dominance

Suppose an agent has von Neumann-Morgenstern preferences over money lotteries that can be represented
by the utility function:
U(p) = Sum[p(x)u(x)],
where
u(x) = − exp(−λx) for some λ > 0.

(a) Derive the agent’s coefficient of absolute risk aversion.

Now suppose for this agent the certain equivalent of an equal-odds (i.e., 50–50) gamble of winning
$1,000 or winning nothing is $470.

(b) What can you say about the certain equivalent of an equal-odds gamble of winning $1,500 or winning $500?

(c) Suppose this agent must choose between
(i) $175 for sure;
(ii) a gamble that will pay $0, $100, $350, or $1000 with probabilities 0.28, 0.5, 0.1, and 0.12, respectively;
(iii) a gamble that is equally likely to pay $0, $100, $200, or $520; and
(iv) a gamble that will pay $0, $100, $200, $400 or $1000 with probabilities 0.25, 0.35, 0.25, 0.05 and 0.1.

i. Find the expected values of the lotteries.
ii. Show that (iii) second order stochastically dominates (iv).
iii. Show that (iv) second order stochastically dominates (ii).
iv. Using that the certain equivalent of an equal-odds (i.e., 50–50) gamble of winning $1,000 or winning nothing is $470, find a lottery such that the agent is indifferent between this lottery and receiving $175 for sure (hint: this lottery can involve the agent sometimes loosing money).
v. Hence argue that the agent most prefers lottery (iii).

I have answered (a), (b) and c(i) but left them there because they may help with the other parts.
Any help would be great, thanks.
Tomgrrad is offline  
 
Reply

  My Math Forum > Science Forums > Economics

Tags
aversion, certainty, dominance, equivalence, risk, stochastic



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Certainty equivalent Pvunderink Calculus 2 February 7th, 2014 02:54 AM
Risk Probability CaseStudy Advanced Statistics 1 November 20th, 2012 02:55 PM
A test to validate pi with 100% certainty Semjase Number Theory 1 September 13th, 2012 01:01 PM
Compound Risk Integration clive37 Calculus 0 March 28th, 2012 01:42 AM
At what chance of winning should I risk $2 for $4? Sparta Advanced Statistics 1 January 20th, 2008 06:35 PM





Copyright © 2019 My Math Forum. All rights reserved.