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Multivariate quadrature (approximation of joint distribution for portfolio choice)

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I would like to numerically compute an optimal portfolio, using multiple assets, which are correlated.
So my question is:
  1. Is there a standard approach for multi-dimensional quadrature? (standard deviation and covariance are sufficient statistics). I only saw this on the file exchange: https://nl.mathworks.com/matlabcentral/fileexchange/13508-multi-dimensional-gauss-points-and-weights
  2. Or is the standard approach to use Monte Carlo simulation, using random draws from a multi-variate distribution (random number generator)
I specifically do not want to use theoretical solutions, but numerical ones.
Many thanks in advance!
  2 Comments
Torsten
Torsten on 16 Nov 2022
Edited: Torsten on 16 Nov 2022
The standard approach is to use "int" for symbolic integration or "integral", "integral2", "integral3" for numerical integration.
Sargondjani
Sargondjani on 17 Nov 2022
@Torsten thank you!! That works very nice, at least upto 3 dimensions... I guess for higher dimensions I'll have to stick with Monte Carlo simulation.

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