2020/06/22 by Eduardo Abi Jaber, Jaber, Eduardo Abi, Enzo Miller +3 · 1 citation
Economics, Econometrics and Finance · Social Sciences · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2006.13539
openalex publication_date 2020/06/22 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/02
This paper concerns portfolio selection with multiple assets under rough\ncovariance matrix. We investigate the continuous-time Markowitz mean-variance\nproblem for a multivariate class of affine and quadratic Volterra models. In\nthis incomplete non-Markovian and non-semimartingale market framework with\nunbounded random coefficients, the optimal portfolio strategy is expressed by\nmeans of a Riccati backward stochastic differential equation (BSDE). In the\ncase of affine Volterra models, we derive explicit solutions to this BSDE in\nterms of multi-dimensional Riccati-Volterra equations. This framework includes\nmultivariate rough Heston models and extends the results of citehan2019mean.\nIn the quadratic case, we obtain new analytic formulae for the the Riccati BSDE\nand we establish their link with infinite dimensional Riccati equations. This\ncovers rough Stein-Stein and Wishart type covariance models. Numerical results\non a two dimensional rough Stein-Stein model illustrate the impact of rough\nvolatilities and stochastic correlations on the optimal Markowitz strategy. In\nparticular for positively correlated assets, we find that the optimal strategy\nin our model is a `buy rough sell smooth' one.\n