In a series of papers, we characterized the value function in optimal control as the unique viscosity solution of the corresponding Bellman equation that satisfies appropriate side conditions. The novelty of our results was that they applied to exit time problems with general nonnegative instantaneous costs, including cases where the instantaneous cost is not uniformly bounded below by positive...

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on part...

A utility maximization problem in an illiquid market is studied. The financial market is assumed to have temporary price impact with finite resilience. After the formulation of this problem as a Markovian stochastic optimal control problem a dynamic programming approach is used for its analysis. In particular, the dynamic programming principle is proved and the value function is shown to be the...

The problem of determining the sequence of a set of jobs with the objective function of minimizing the maximum earliness and tardiness in one machine is studied. &#10 Production systems like JIT are one of the many applications of the problem. This problem is studied in special cases and their optimal solutions are introduced with simple orders. In general, some effective conditions for ne...

In this paper, Economic Order Quantity ( ) based model for non-instantaneous deteriorating items with imperfect quality, permissible delay in payments and inflation is proposed. We adopt a time-dependent demand function. Also, the effects of time value of money are studied using the Discounted Cash Flow approach. Moreover, we assume that orders may contain a random proportion of defective items...

The paper is concerned with fully nonlinear second order Hamilton{Jacobi{Bellman{ Isaacs equations of elliptic type in separable Hilbert spaces which have unbounded rst and second order terms. The viscosity solution approach is adapted to the equations under consideration and the existence and uniqueness of viscosity solutions is proved. A stochastic optimal control problem driven by a paraboli...

Preface These are the extended version of the Cattedra Galileiana I gave in April 2003 in Scuola Normale, Pisa. I am grateful to the Society of Amici della Scuola Normale for the funding and to Professors Maurizio Pratelli, Marzia De Donno and Paulo Guasoni for organizing these lectures and their hospitality. In these notes, I give a very quick introduction to stochastic optimal control and the...

We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary (gij(t, x) ≥ 0). We show existence of the optimal strategy, and give when the optimal strategy is finite via a verification theorem. Finally, when the state of the system is a markov process, we show that the vector of value functions of ...

We revisit the pioneering work of Bressan & Hong on deterministic control problems in stratified domains, i.e. control problems for which the dynamic and the cost may have discontinuities on submanifolds of R . By using slightly different methods, involving more partial differential equations arguments, we (i) slightly improve the assumptions on the dynamic and the cost; (ii) obtain a compariso...