Hiroaki Morimoto

Dynkin games and martingale methods

We consider non-Markov stochastic games with stopping times, so-called Dynkin games. Using the martingale point of view, we show the existence of a saddle-point under general assumptions

On average cost stopping time problems

SummaryWe consider the stopping time problems whose costs are given by time average forms, a generalization of the Gittins index. We show the existence of the optimal solutions and give their approximation to these stopping time problems.

Variational Inequalities for Combined Control and Stopping

We study the variational inequality associated with the combined stochastic control problem and establish the existence of a unique viscosity solution without uniform ellipticity. An application to the quasi-variational inequality is given.

Ergodic Control Of Stochastic Differential Systems With Controller Constraints

We consider the ergodic control problem for stochastic differential systems with controller constraints. The corresponding Bellman equation is solved rigidly in C 2-class to obtain both the minimal value and the optimal control

Adaptive LQG regulator via the separation principle

The continuous-time linear quadratic adaptive control problem with average cost per unit time is studied. It is shown that a consistent estimator of an unknown parameter and the optimal control can be obtained by using the separation principle, which decomposes the problem into two parts: to find the consistent estimator in the case without controls; and to solve the Riccati equation in the LQ regulator problem with the parameter estimate replacing the unknown parameter. >

Stochastic Control and Mathematical Modeling: Applications in Economics

This is a concise and elementary introduction to stochastic control and mathematical modeling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and nonlinear PDE theory.

Attractors of probability measures for semilinear stochastic evolution equations

We consider the chaotic behavior of solutions of semi1inear stochastic evolution equations.We prove the existence of the largest attractor of probability measures to which the Markovian transition probabi1ity converges

Optimal Consumption in a Growth Model with the Cobb-Douglas Production Function

An optimal consumption problem is studied in a growth model for the Cobb-Douglas production function in a finite horizon. The problem is transferred into a stochastic Ramsey problem so as to reduce the dimension of the state space. The corresponding state equation is a stochastic differential equation with inherently non-Lipschitz coefficients, whose unique solvability is established. The unique existence of the classical solution of the Hamilton-Jacobi-Bellman equation associated with the original problem is proved, and a synthesis of the optimal consumption policy is presented in the feedback form.

Optimal switching for alternating processes

This paper is concerned with the problems of optimal switching for general stochastic processes. We show the existence of the maximal element of a class of dynamic programming inequalities by the method of impulsive control. We obtain results on the existence of optimal control for general and cyclic switching problems.

A Singular Control Problem with Discretionary Stopping for Geometric Brownian Motions

In this paper, we discuss a combined singular control problem with discretionary stopping for geometric Brownian motions. By the method of penalization, we solve the degenerate variational inequality associated with this problem. Its solution