Relaxing the sure-solvency conditions in temporary equilibrium models
Temporary equilibrium models typically assume that each trader voluntarily chooses from only those futures contracts that involve zero probability of bankruptcy, and sometimes an institution imposes an additional sure-solvency constraint (from its viewpoint). The focus of this paper is on the robustness of the temporary equilibrium results to relaxation of these sure-solvency conditions. The model is a two-stage securities market in which a ''security'' is a contract to deliver a specified commodity in the second stage. Second- stage utility is a function of second-stage wealth. Preferences over bankrupt states are represented by extending the indirect utility function to negative wealth. In the first stage, a portfolio of securities is selected to maximize expected utility given first-stage security prices and probability distributions of second-stage commodity prices. When short sales are unimpeded by institutional constraints, a necessary condition for existence of temporary equilibrium is that the interior of the supports of the probability measures have a non-empty intersection. If, in addition, for all individuals the extended indirect utility approaches -\(\infty\) as wealth approaches -\(\infty\), then the usual temporary equilibrium results hold, even though the expected utility function may fail to be continuous. In contrast, if for some individual the indirect utility function is bounded below, then temporary equilibrium may fail to exist due to empty demand correspondences [an example is provided]. When short-sales are regulated by an institutional sure-solvency condition, it is well-known that temporary equilibrium exists even without overlapping supports. This paper shows that, provided institutional expectations are sufficiently broad, the institutional sure-solvency condition can be replaced by less stringent conditions such as a limit on the maximum loss or expected loss.
scientific article; zbMATH DE number 3926587