Optimal Portfolio Optimization with options/derivatives

[Dibalias]

Hi,

I'm facing an delicate issue. I'm searching for method/papers on the optimal allocation of a portfolio with stocks, options and risk-free asset. I know it's a very difficult problem but i'm sure some of you encountered it before.

Thank you.

 

[pingu]

Search for Differential Evolution.

 

[Dibalias]

Thanks that's big help. I found out about the so called Genetic Algorithm in my research, but i wasn't aware of such generalization. I'll look about it.

But i was expecting a more formal model, like a Markowitz-style optimization or some application of stochastic control.

 

[pingu]

Thanks that's big help. I found out about the so called Genetic Algorithm in my research, but i wasn't aware of such generalization. I'll look about it.

But i was expecting a more formal model, like a Markowitz-style optimization or some application of stochastic control.

Try new things.

If you were expecting something, it means you had a preconceived idea and were looking for validation.

 

[Dibalias]

Try new things.

If you were expecting something, it means you had a preconceived idea and were looking for validation.

You're right. Thanks !

 

[yetanotherquant]

"Optimal Portfolio Optimization" sounds tautological but indeed it is a very good question: which optimization criteria is "more optimal" than (all) others.
In a sense it is the Kelly criterion, which beats all other approaches in the long run (But beware, in the long run we are all dead - J.M. Keynes).
In this sense, I recommend you to have a look at my paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2259133

As to concrete (numerical) optimization, my approach may (and likely will) work for you.
However, it may fail because you have options => (very) heavy-tailed distribution of returns.