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I'm using modern portfolio theory to compute the frontier of efficient portfolios. I'd like to pick the best one in the spirit of Kelly betting, ie. maximising expected growth.

I'm looking for a reference that describes rigorously how I'd go about doing this.

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Maybe you will find the following papers pretty interesting:

Laureti, P., Medo, M., and Zhang, Y.-C. (2010). Analysis of Kelly-optimal portfolios. Quantitative Finance, 10(7): 689–697.

and

Nekrasov, Vasily, Kelly Criterion for Multivariate Portfolios: A Model-Free Approach (September 30, 2014).

The last one is available at SSRN.

Particularly, the last one shows how to apply the Kelly Criterion to stock portfolios.

Of course, in my humble opinion, you have to keep attention to what you are going to apply the model for and to the underlying hypothesis; such hypothesis, as, for instance, the joint normally distributed stock returns assumption, are pretty strong for an application of such strategy to the realty.

Hope this helps.

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