My Math Forum  

Go Back   My Math Forum > Science Forums > Economics

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

LinkBack Thread Tools Display Modes
May 10th, 2017, 12:45 PM   #1
Joined: Dec 2016
From: Germany, Magdeburg

Posts: 3
Thanks: 0

Lebesgue-Stieltjes integrals, lower partial moments, probability distributions

Working through a lecture in performance management course (topic about downside-oriented risk measures and lower partial moments), I have encountered several expressions of the following form:


where F(R) is the cumulative distribution function, E is the expectation, LPM is the lower partial moment

or, for example,

LPM(2,t)(R)=t*(2*LPM(1,t)(R) - t*LPM(0,t)(R)) + integral(R^2dF(R))

It was also mentioned in one article that the integrals are of Lebesgue-Stieltjes type.

I was not taught anything like this either at university or at school, so I would ask you to provide any links to books/chapters from books/articles from where I can fill this gap in knowledge. I want to be able to understand the above transformations and conduct them on my own, I also would like to cover the whole theory behind this. Also, how large is the volume of theory I have to cover, given that I only made some simple integral calculus at school? Thank you very much.

Last edited by skipjack; May 10th, 2017 at 09:08 PM.
knownothing1994 is offline  

  My Math Forum > Science Forums > Economics

distributions, integrals, lebesgue, lebesguestieltjes, lebesguestiljets, lower, moments, partial, probability, stiljets

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Free Source Code for moments of path integrals of a Stochastic Process AhsanAmin Advanced Statistics 0 December 10th, 2014 03:43 PM
Why don't double integrals use a partial differential? boogyman19946 Differential Equations 8 July 13th, 2012 08:35 AM
Partial Fractions to find Integrals chapsticks Calculus 1 February 26th, 2012 09:56 AM
Calculate distributions lower quartile,median, higher quarti Riazy Advanced Statistics 0 March 8th, 2011 12:50 PM
Riemann and lebesgue integrals bromaze Real Analysis 1 February 16th, 2010 01:47 PM

Copyright © 2017 My Math Forum. All rights reserved.