We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk...

This paper analyzes equilibrium in a dynamic pure-exchange economy under a generalization of Merton's (1987) investor recognition hypothesis (IRH). Because of information costs, a class of investors is assumed to possess incomplete information, which suffices to implement only a particular...

We consider optimization problems involving coherent risk measures. We derive necessary and sufficient conditions of optimality for these problems, and we discuss the nature of the nonanticipativity constraints. Next, we introdice dynamic risk measures, and we formulate multistage optimization...

We introduce an axiomatic definition of a conditional convex risk mapping. By employing the techniques of conjugate duality we derive properties of conditional risk mappings. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We...

This article studies an economy with borrowers (firms or individuals) under costly default. Borrowers defaulting under adverse economic conditions may, despite incurring default costs, emerge as wealthier than nonborrowers. Asset substitution is generally not pronounced, although a larger risk...

This article analyzes a dynamic general equilibrium under a generalization of Merton's (1987) investor recognition hypothesis. A class of informationally constrained investors is assumed to implement only a particular trading strategy. The model implies that, all else being equal, a risk premium...

For testing the equality of variances for correlated variables, Harris (1985) suggested Wald type test statistics. In this note we show that this test coincides with the generalized least squares statistic employed in the analysis of covariance structures. We derive the generalized least squares...