In this paper, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective.
We generalize the results of Bielecki and Rutkowski (2015) on funding and collateralization to a multi-currency framework and link their results with those of Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b).
We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes).
Furthermore we analyse the relationship between the long-term swap rate, the long-term yield, see Biagini et al. , Biagini and H\"artel , and El Karoui et al. , and the long-term simple rate, considered in Brody and Hughston  as long-term discounting rate.