Hi All,I am stuggling to understand what this question is trying to get at..Let X~N(0,1) a normally distributed random variable mu = 0, sigma = 1. suppose now x E R, x >0 find the upper and lower bound of the conditional expectation of X for E(X|X>=x)Here X and x are different and not a typo.First thoughts was to just compute the integral with the limits 0<x<infinity but this obviously leads to just a number, and no inequality. I then started treating the two parts X and X>=x as two random variables not really much help there either.. My final thoughts was looking at the known inequalities such as Chebyshev's inequality etcand these tend to be single bound from above... Im not looking for the solution by any means just a gentle push in the right direction please..

I think you need to first find a conditional probability for Xand compute the expectationThis will give the expectation as a function of x, then find the bounds ofthat function?The problem on pp.40 of Zhou's book is solved for x=0 case with a smallmistake which was addressed by him on the book's website.

Basically, this is Expected Shortfall for a standard normal variable. This is dealt with, for example, in Embrechts/Frey/McNeil - Quantitative Risk Measurement, Example 2.18.

The conditional probability density function is when X > x and 0 otherwisewhere f is the normal pdf and N is the normal cdf.You can use this to find the expectation in the standard fashion.

P(R<r) = P(X<r & X>a)/P(X>a) = P(X<r)*I(r>a)/(1-Phi(a))=> f_R = f_x(r)/(1-Phi(a))*I(r>a)integrate from a to inf x*f_X = exp(-a^2/2)/sqrt(2*pi)i.e.E R = exp(-a^2/2)/(sqrt(2*pi)*(1-Phi(a))Tested it; seems to be right. Edit: Should have refreshed the page before posting (thus seeing bwarrens post), given the activity here lately I did not think that it would be necessary...

Right, the expectation iswith f the normal pdf and N the normal cdf.

Cheers guys for the hints. I have had a look at cdfs now, and looking at the problem again I think the "survival" test is the route forward in obtaining some limit to the conditional expectation. Once again thankyou for the help..

On the same subject, you can compute quantities like E(W_t|W_s > 0) where 0<s<t and W_t is a standard BM.

Hi all, I have a question that is related to the subject, it comes from wider problem but getting some clarity in this question would help solve the original one. Could anyone tell me what is the value ( a brief demonstration would be really appreciate) of E[dW_t | S_T] where T>t and S_t is a conventional GBM.Thank you very much.

QuoteHi all, I have a question that is related to the subject, it comes from wider problem but getting some clarity in this question would help solve the original one. Could anyone tell me what is the value ( a brief demonstration would be really appreciate) of E[dW_t | S_T] where T>t and S_t is a conventional GBM.Thank you very much.

Even though I accept the criticism I consider rude to categorize me as a Trol... please, I only behave with one of the 9 possible behaviors of the troll, in this scenario and considering that I am new, perhaps ingenuity or simply ignorance in how to approach this forum may apply. I genuinely believed that my question applied to the topics whose forums I wrote.

QuoteOriginally posted by: pgarciajaramilloEven though I accept the criticism I consider rude to categorize me as a Trol... please, I only behave with one of the 9 possible behaviors of the troll, in this scenario and considering that I am new, perhaps ingenuity or simply ignorance in how to approach this forum may apply. I genuinely believed that my question applied to the topics whose forums I wrote.**Joined: Jun 2012 Fair enough. Maybe 'spammer'. But trollers use 'flooding by excessive posting' and 'violating policies', and these are well known on Wilmott. ...But 9 times the same question is kind of unique. What's the rationale for doing this? Plan B is to create your own thread just ONCE and let people respond if and when they want.

Yes, now it is clear to me how to approach the forum. I didn't have in mind the policies (being one year since I signed in). Yesterday being really the first time using it, I had a different expectation about the dynamics of the forum that led me to spread my question as much as I could between the discussions whose genders I thought applied. I am sorry, it wasn't mi intention to disrupt the environment of the forum.

The test is:If pgarciajaramillo is not his name then he might be a troll.If pgarciajaramillo is his real name then he's not very smart, but not a troll.P

Haha, unfortunately... is the second one.