Optimization Question

I wanted to be able to generally include a non-linear constraint on an 
optimization. I was using maxdrawdown, var, or any risk measure as 
examples.

Real world example might be when one needs to optimize a portfolio 
with weight constraints (max size to one or more securities).  We 
might choose a utility function such as info ratio, calmar ratio, etc, 
but the resulting solution, while wonderful from utility perpective, 
has poor real world pnl and isn't simply scalable due to weight 
constraints. One can modify the utility function, or constrain the 
risk (or profit) to some minimum. 
So generally investigating optimization with potentially non-linear 
constraints. I think a penalty function into utility is best but 
wondering if there were other approaches.

Ian McDonald


----- Original Message -----
From: Patrick Burns [patrick at burns-stat.com]
Sent: 12/30/2008 09:01 PM GMT
To: Ian McDonald
Cc: r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] Optimization Question



I suspect that including Maximum drawdown in an
optimization is unlikely to be useful.  However, I'm
anxious to be proven wrong.

It's not clear to me what specifically you are wanting
to do, but Manfred Gilli has done a fair amount on
VaR in optimization. (But I don't think you'll get any
R code off him.)

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

ian.mcdonald at malbecpartners.com wrote:

I am interested in doing a portfolio optimization, but I need to 
impose non-linear, functional constraints (i.e Max Drawdown, or VaR, 
etc). I've looked into several of the optimization routines (nlminb, 
constrOptim and optim with SANN/L-BFGS-B) but it appears that all of 
them are geared to linear constraints. Other than using a penalty 
function method, is anyone aware of any other approaches available 
in  R?

Thanks
Ian McDonald
Malbec Partners

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