"Problems Book to Accompany Mathematics for Economists" is intended to complement any course in quantitative methods in economics, mathematical economics for undergraduate students or introductory mathematical economics for graduate students. It is aimed as an inexpensive supplement to nearly...

In this paper, we state sufficiency, necessity, convergence, existence and uniqueness results for infinite horizon optimal control problems with unbounded payoffs in which the assumptions are very weak and there are no topological assumptions about the model components. We also state a sequence...

This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a...

This paper provides a concise guide to dynamic optimization with an integral treatment on various optimal control and dynamic programming problems. It presents essential theorems and methods for obtaining and characterizing solutions to these problems. The paper discusses Pontryagin's maximum...

This is the partial manuscript of a book developing the tools of nonstandard analysis, geared to applications in mathematical economics. It was written over the period 1993-2008. There is no plan to complete and publish it

This note proves existence of a unique equilibrium in a Lucas (1978) economy when the utility function displays constant relative risk aversion and log dividends follow a normally distributed AR(1) process with positive auto-correlation. In particular, the note provides restrictions on the...

Monitoring is an important and costly activity in resource management problems such as containing invasive species, protecting endangered species, preventing soil erosion, and regulating contracts for environmental services. Recent studies have viewed optimal monitoring as a Partially Observable...

This paper describes a method for solving a class of forward-looking Markov-switching Rational Expectations models under noisy measurement, by specifying the unobservable expectations component as a general-measurable function of the observable states of the system, to be determined optimally...

Referring to the literature on optimal stopping under sequential sampling developed by Chernoff and collaborators, we solve a dynamic model of the economic evaluation of a new health technology, deriving optimal rules for technology adoption, research abandonment and continuation as functions of...

We develop a contingent claims model of a firm in financial distress with a formal account for renegotiations under the Chapter 11 bankruptcy procedure. Shareholders and two classes of creditors (senior and junior) alternatively propose a reorganization plan subject to a vote. The bankruptcy...