The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk … averse variational preferences. No-arbitrage conditions are given in terms of risk adjusted priors. A sufficient condition … for existence of efficient allocations is the overlapping of the interiors of the risk adjusted sets of priors or the …

We create an analytical structure that reveals the long-run risk-return relationship for nonlinear continuous … eigenfunction term. The eigenvalue encodes the risk adjustment, the martingale alters the probability measure to capture long … components of cash flows induce changes in the corresponding eigenvalues and eigenfunctions, we reveal a long-run risk …