Help understanding this formula: Risk Parity Algorithm

[Nicolas Galarza Ricci]

Hello everybody!
I am trying to understand an optimization algorithm to achieve risk parity in a portfolio. I need some help figuring out the notation in the following formula:

I found this on THIS paper.

I understand the following, if you could help me by pointing any mistake, would be great!

I understand that this algorithm is suppossed to iterate the allocation for each asset at a time.

x*i : The iteration n+1 of asset i.

σi : The standard deviation of Asset i

xj : allocation for each asset j

σj : The standard deviation of asset j

ρi,j : This is my biggest question. WHAT is this?

bi : THe risk budget for the asset, which for risk parity is 1/n

σ (x) : The standard deviation of the portfolio

What am I missing? Thank you VERY MUCH guys!

 

[Le Van]

ρi,j is the correlation coefficient between returns of asset i and asset j.

 

[Nicolas Galarza Ricci]

Thank you Le Van. I think I got it now, it took a while but I think I solved it. As soon as I confirm it´s working I´ll share the answer here!