Lagrange multiplier methods are standard fare in elementary calculus courses, and they play a central role in economic applications of calculus because they often turn out to have interpretations as prices or shadow prices. You have seen them generalized to cover dynamic, non-stochastic models as Hamiltonian methods, or as byproducts of using Pontryagin’s maximum principle. In static models Lag...

We study a dynamic stochastic general equilibrium model in continuous time. Related work has proven that optimal consumption in this model is a smooth function of state variables. This allows us to describe the evolution of optimal state variables (wealth and labour market status) by stochastic di¤erential equations. We derive conditions under which an invariant distribution for state variables...

This paper discusses uniqueness of user equilibrium in transportation networks with heterogeneous commuters. Daganzo (1983, Transportation Science) proved the uniqueness of (stochastic) user equilibrium when commuters have heterogeneous tastes over possible paths but identical disutility functions from time costs. We Þrst show, by example, that his result may not apply in general networks if di...

In this paper we propose a composite Variational Inequality formulation for modeling multi-mode, multi-class and multi-criteria stochastic dynamic user equilibrium problem in recurrent congestion network with queues. The each mode of travelers is classified into two classes. One is the equipped traveler following stochastic dynamic user-equilibrium with less uncertainty of travel cost, another ...

In this paper we propose a composite Variational Inequality formulation for modeling multimode, multi-class stochastic dynamic user equilibrium problem in recurrent congestion networks with queues. The modes typically refer to different vehicle types such as passenger cars, trucks, and buses sharing the same road space. Each vehicle type has its own characteristics, such as free flow speed, veh...

This paper studies the implications of model uncertainty under stochastic volatility model for equilibrium asset pricing. We derive the equilibrium equity premium and risk-free rate in a pureexchange economy with one representative agent who is averse not only to risk but also to model uncertainty. The results show that robustness increases the equilibrium equity premium while lowers the risk-f...