The ultra long run (ULR) discount rates are key inputs for valuing pension funds, life annuities, or firms with long run investments due to low carbon transition. However the corresponding zero-coupon bonds are only actively traded up to a last liquid point (LLP) such as 20 years, say. This...

In modeling disequilibrium macroeconomic systems which one would want to subject to econometric estimation one typically faces the problem of whether the structural model can determine a unique equilibrium. The problem inherits a special form because the regimes in which the equilibria can lie...

This paper analyzes the risks in random sets and their implications for basket derivatives. Based on an extension of integration by parts for random set, we define stochastic dominance of order 1 and 2 for random sets. Since the ordering of sets, that is the inclusion, is a partial order, we...