# Solving a LogNormal Conditional expectation equation - Insurance

#### OLSMAG

##### New Member
Hi everyone,

I am a newbie here and apologize if this post is in the wrong forum.

I need help to solve the following LogNormal Conditional expectation equation for MuNew such that:

(e^(MuNew + Sigma^2/2)*normcdf((-log(LowerLimit)+MuNew+Sigma^2)/Sigma))
/
(1-logncdf(LowerLimit, MuNew, Sigma)) - Severity = 0.0001

normcdf = Standard Normal cumulative distribution function. Hence Mu = 0, Sigma =1
logncdf= Lognormal cumulative distribution function

Is there any pros out there that can help me?

Thanks!!

Br, Magnus #### Dason

So all the parameters but MuNew are fixed known quantities?

#### Dason

Solver in Excel should be able to do this kind of thing. Otherwise if you move everything to one side equation then ultimately you're just looking the zeroes/roots of the resulting expression and most math/stats packages have root solvers easily available. Are you using any particular software for this?

#### OLSMAG

##### New Member
Solver in Excel should be able to do this kind of thing. Otherwise if you move everything to one side equation then ultimately you're just looking the zeroes/roots of the resulting expression and most math/stats packages have root solvers easily available. Are you using any particular software for this?
I am using MATLAB to solve this by running through loops. Could use Solver but it's also based on loops. Thus I want to skip the looping part.

Is it possible for you to help me solve this equation? I don't have any software other than MATLAB and Excel.