Maria B. Chiarolla

On a Stochastic, Irreversible Investment Problem

The productive sector of the economy, represented by a single firm employing labor to produce the consumption good, is studied in a stochastic continuous time model on a finite time interval. The firm must choose the optimal level of employment and capital investment in order to maximize its expected total profits. In this stochastic control problem the firms capacity is modeled as an Ito process controlled by a monotone process, possibly singular, that represents the cumulative real investment. It is optimal to invest when the shadow value of installed capital exceeds the capitals replacement cost; this threshold is the free boundary of a related optimal stopping problem which we recast as a stopping problem without integral cost, similar to the American option problem. Then, under a regularity condition, we characterize the free boundary as the unique solution of a nonlinear integral equation.

Optimal Control of Inflation: A Central Bank Problem

This paper models the action of the central bank on the dynamics of the nominal interest rate with the aim of controlling inflation. The problem is set up as a two-dimensional bounded variation control problem; it is shown that its variational formulation leads to a stochastic differential game with stopping times between the conservative and the expansionist tendencies of the bank.

The Free Boundary of the Monotone Follower

This paper identifies the free boundary arising in the two- dimensional monotone follower, cheap control problem. It proves that if a region of inaction

Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment Under Limited Resources

\cal A

Equilibrium in a stochastic model with consumption, wages and investment

is of locally finite perimeter (LFP), then

Multivariable Utility Functions

\cal A

Managing inflation: a control problem

can be replaced by a new region of inaction

Explicit Solution of a Stochastic, Irreversible Investment Problem and Its Moving Threshold

\tilde{\cal A}

Controlling Inflation: The Infinite Horizon Case

whose boundary is locally

Optimal Dynamic Procurement Policies for a Storable Commodity with Levy Prices and Convex Holding Costs

C^1