Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I want to calculate the expectation and variance in the following scenario:

$w$ is my initial wealth

With probability $0< q_i <1$ with$ i \in\{a,b,c\}$ I lose $a,b$ or $c$ repectively.

$U()$ is a concave utility function, so with probability $q_a$ my utility is $U(w-a)$

I think I can calculate the expected utility via:

$E(U) = q_a(U(w-a))+q_b(U(w-b))+q_c(U(w−c)) $

but I have no idea how to calculate the variance. Any hints on that?

share|cite|improve this question
Variance? X? U? pi? Indications about what you tried? – Did Feb 22 '13 at 14:43
Can you please your notation? – Mohan Feb 22 '13 at 16:03
@Did: I edited my question to make it more clear – Tom Feb 22 '13 at 16:45
up vote 0 down vote accepted

The formula for the expected utility $E(U)$ is correct.

Using $E(U)$ the variance can be obtained by: $\sigma^2=q_a\cdot(U(w-a)-E(U))^2+q_b\cdot(U(w-b)-E(U))^2+q_c\cdot(U(w-c)-E(U))^2$

or alternatively by: $\sigma^2=E(U^2)-[E(U)]^2$

with $E(U^2)=q_a\cdot [U(w-a)]^2+q_b\cdot[U(w-b)]^2+q_c\cdot[U(w-c)]^2$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.