# Thread: Solving a LogNormal Conditional expectation equation - Insurance

1. ## Solving a LogNormal Conditional expectation equation - Insurance

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

2. ## Re: Solving a LogNormal Conditional expectation equation - Insurance

What is LowerLimit?

3. ## Re: Solving a LogNormal Conditional expectation equation - Insurance

Originally Posted by Dason
What is LowerLimit?
Hi,

LowerLimit = Deductible i.e. a number greater than 0.

4. ## Re: Solving a LogNormal Conditional expectation equation - Insurance

So all the parameters but MuNew are fixed known quantities?

5. ## Re: Solving a LogNormal Conditional expectation equation - Insurance

Originally Posted by Dason
So all the parameters but MuNew are fixed known quantities?
Yes, that's correct.

6. ## Re: Solving a LogNormal Conditional expectation equation - Insurance

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?

7. ## Re: Solving a LogNormal Conditional expectation equation - Insurance

Originally Posted by 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?
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.

8. ## Re: Solving a LogNormal Conditional expectation equation - Insurance

I mean I don't think there is a closed form solution for what you want so any method to solve will be iteration based. With matlab I wouldn't think you would need to explicitly write out the loops by hand though.

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