Markowitz Portfolio Selection for Multivariate Affine and Quadratic Volterra Models

This paper concerns portfolio selection with multiple assets under rough covariance matrix. We investigate the continuous-time Markowitz mean-variance problem for a multivariate class of affine and quadratic Volterra models. In this incomplete non-Markovian nonsemimartingale market framework unbounded random coefficients, optimal strategy is expressed by means Riccati backward stochastic differential equation (BSDE). case models, we derive explicit solutions to BSDE in terms multidimensional Riccati--Volterra equations. includes Heston models extends results Han Wong [Appl. Math. Optim. (2020)]. case, obtain new analytic formulae establish their link infinite-dimensional covers Stein--Stein Wishart type Numerical on two-dimensional model illustrate impact volatilities correlations strategy. particular positively correlated assets, find that our “buy sell smooth” one.