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explicit


Total Posts: 26
Joined: Sep 2005
 
Posted: 2018-06-12 18:07
I am writing a paper on trading multiple mean reverting assets. From mathematical point of view it is an optimal control problem of n correlated OU processes, and one needs to find an optimal trading rule to maximize the utility function of the final wealth.

I am interested in the practical aspects of the above. Shall I consider this problems over a final horizon, or perpetual is also fine from the practical point of view? What do you think about the use of utility functions? etc



ronin


Total Posts: 343
Joined: May 2006
 
Posted: 2018-06-13 14:41
It doesn't sound like a particularly interesting problem, tbh. There must be dozens of people here who can give you the solution without bothering to solve a single equation. And assets that you can trade are never mean reverting anyway.

Practically, you can only optimize final wealth over a finite horizon. If infinite horizon, it would have to be annual return (per unit of capital, or per unit of volatility etc), or something like that. And you would have to worry about hitting zero capital etc. You probably also want some penalty terms in your utility function to eliminate strategies that are too weird.


"There is a SIX am?" -- Arthur

Azx


Total Posts: 37
Joined: Sep 2009
 
Posted: 2018-06-13 15:15
Use an isoelastic function for utility and you won't have to worry about time horizon. It is not clear what the purpose of your paper is, there are already plenty of papers that derive the optimal portfolio for a variety of utility functions. Are you writing a thesis?

rickyvic


Total Posts: 125
Joined: Jul 2013
 
Posted: 2018-06-27 19:02
I agree with Ronin

Btw I would look at a way to integrate the expected returns of the ou processes in a portfolio model, perhaps with a closed form solution?
I am sure there is a ton of stuff on the matter although I havent research it.

It is definitely of practical interest in a descrete time one step ahead (or multiple horizons) setting

"amicus Plato sed magis amica Veritas"

doctorwes


Total Posts: 577
Joined: May 2005
 
Posted: 2018-06-27 21:51
Is this the kind of thing you have in mind?

Application of the Kelly criterion to Ornstein-Uhlenbeck processes



rickyvic


Total Posts: 125
Joined: Jul 2013
 
Posted: 2018-07-02 11:25
Yes it is one way to look at it.

"amicus Plato sed magis amica Veritas"
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