2024/01/01 by Dominguez, Alejandro Rodriguez · 1 citation
#35A35 #58J65 #91G10 #91G30 #91G60 #91G70 #93C20 #FOS: Economics and business #G.1.8 #G.3 #J.4 #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM)
paper · doi:10.48550/arxiv.2401.00949
Portfolio's optimal drivers for diversification are common causes of the constituents' correlations. A closed-form formula for the conditional probability of the portfolio given its optimal common drivers is presented, with each pair constituent-common driver joint distribution modelled by Gaussian copulas. A conditional risk-neutral PDE is obtained for this conditional probability as a system of copulas' PDEs, allowing for dynamical risk management of a portfolio as shown in the experiments. Implied conditional portfolio volatilities and implied weights are new risk metrics that can be dynamically monitored from the PDEs or obtained from their solution.