  In the aftermath of the 2007 global financial crisis, banks started
reflecting into derivative pricing the cost of capital and collateral funding
through XVA metrics. Here XVA is a catch-all acronym whereby X is replaced by a
letter such as C for credit, D for debt, F for funding, K for capital and so
on, and VA stands for valuation adjustment. This behaviour is at odds with
economies where markets for contingent claims are complete, whereby trades
clear at fair valuations and the costs for capital and collateral are both
irrelevant to investment decisions. In this paper, we set forth a mathematical
formalism for derivative portfolio management in incomplete markets for banks.
A particular emphasis is given to the problem of finding optimal strategies for
retained earnings which ensure a sustainable dividend policy.
