Stochastics Seminar - Saeed Khalili

Saeed Khalili, Department of Mathematics, University of Colorado Boulder

Optimal Consumption in the Stochastic Ramsey Problem without Boundedness Constraints
 

This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity nor linear growth, specifies the dynamics of the controlled state process. A mixture of probabilistic arguments are used to construct the state process, and establish its non-explosiveness and strict positivity. This leads to the optimality of a feedback consumption process, defined in terms of the value function and the state process. Based on additional viscosity solutions techniques, we characterize the value function as the unique classical solution to a nonlinear elliptic equation, among an appropriate class of functions. This characterization involves a condition on the limiting behavior of the value function at the origin, which is the key to dealing with unbounded consumptions. Finally, relaxing the boundedness constraint is shown to increase, strictly, the expected utility at all wealth levels.

 

(Joint work with Yu-Jui Huang)

Thursday, November 29, 2018 at 11:00am to 12:00pm


Engineering Center, ECOT 226
1111 Engineering Drive, Boulder, CO 80309

Event Type

Colloquium/Seminar

Interests

Science & Technology, Research & Innovation

Audience

Faculty, Students, Graduate Students, Postdoc

College, School & Unit

Engineering & Applied Science

Group
Applied Mathematics
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