Jose Luis Menaldi

On an Investment-Consumption Model With Transaction Costs

This paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and

ADDITIVE CONTROL OF STOCHASTIC LINEAR SYSTEMS WITH FINITE HORIZON.

n

Second Order Elliptic Integro-Differential Problems

risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a variational inequality for the value function. Existence and uniqueness of a viscosity solution are proved. The variational inequality is solved by using a numerical algorithm based on policies, iterations, and multigrid methods. Numerical results are displayed for

Optimal Control of Stochastic Integrals and Hamilton–Jacobi–Bellman Equations. I

n=1

On the Optimal Impulse Control Problem for Degenerate Diffusions

and

On the Optimal Stopping Time Problem for Degenerate Diffusions

n=2

Optimal correction problem of a multidimensional stochastic system

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Optimal control and differential games with measures

We consider a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients. The control acts additively on the state of the system. Our objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of an appropriate free boundary problem in a space-time domain. By using some decomposition arguments, the problems of a two-sided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be reduced to a simpler case of only one-sided control, i.e. a monotone follower. These results are applied to solving some examples by the so-called method of similarity solutions.

Singular ergodic control for multidimensional Gaussian processes

PREFACE GLOSSARY OF BASIC NOTATIONS ELLIPTIC EQUATIONS Background Problems Not in Divergence Form Problems in Divergence Form Markov-Feller Processes INTEGRO-DIFFERENTIAL OPERATORS Discussion The Whole Space Bounded Domains Adjoint Operators Unbounded Functions and Commutator Relation with Jump Processes INTEGRO-DIFFERENTIAL EQUATIONS Problems Not in Divergence Form Problems in Divergence Form GREEN FUNCTION ESTIMATES Discussion Basic Properties Green Spaces Dirichlet Boundary Conditions INVARIANT DENSITY MEASURE Discussion Ergodicity Asymptotic Behavior Boundary Singularity STOPPING TIME PROBLEMS Discussion Setting of the Problem Variational Inequality Asymptotic Behavior ERGODIC CONTROL PROBLEMS Stochastic Control Hamilton-Jacobi-Bellman Equation BIBLIOGRAPHY INDEX

Exponential estimates in exit probability for some diffusion processes in hilbert spaces

We consider the solution of a stochastic integrals control problem. In particular, we characterize the optimal cost as the maximum subsolution of the Hamilton-Jacobi-Bellman equation with Dirichlet boundary conditions. We also prove some regularity results for the optimal cost.