We study finite horizon optimal stopping problems for continuous time Feller-Markov processes. The functional depends on time, state and external parameters, and may exhibit discontinuities with respect to the time-variable. Both left and right-hand discontinuities are considered. We investigate the dependence of the value function on the parameters, initial state of the process and on the stop...

The Wiener disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of ’disorder’ when the drift of an observed Wiener process changes from one value to another. In this paper we present a solution of the Wiener disorder problem when the horizon is finite. The method of proof is based on reducing the initial problem to a parabolic free-boundary pro...

In this paper we introduce the threshold risk measures, a class of risk measures incompatible with the coherent risk measures. In particular, the threshold risk measures consider the risk involved in applications where being above a threshold (for minimization problems) is considered too risky and should be avoided as much as possible. In this paper we develop the threshold risk measures togeth...

We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and completely solved using probabilistic tools such as the Snell envelop of processes and reflected backward stochastic differential equations. Finally, whe...

When a prisoner’s-dilemma-like game is repeated any finite number of times, the only equilibrium outcome is the one in which all players defect in all periods. However, if cooperation among the players changes their perception of the game by making defection increasingly less attractive, then players may be willing to cooperate in late periods in which unilateral defection has become unprofitab...

In this paper, we study the problem of finite-horizon Kalman filtering for systems involving a norm-bounded uncertain block. A new technique is presented for robust Kalman filter design. This technique involves using multiple scaling parameters that can be optimized by solving a semidefinite program. The use of optimized scaling parameters leads to an improved design. A recursive design method ...

In this paper we show that any surface in R3 can be modified by gluing on small ‘focusing caps’ so that its geodesic flow becomes ergodic. A new concept, finite horizon cap geometry, is what makes the construction work.

We consider a periodic review inventory system and present its optimal policy in the infinite horizon setting. The optimal inventory policy that maximizes the infinite horizon expected discounted profit for the model is analytically obtained by relating to the finite horizon setting using results from variational analysis. Results are provided that elucidate the operations of the inventory syst...

A typical discrete-time sequential decision problem involves a system whose state is assumed to evolve either deterministically or probabilistically over time-periods that are often called stages. This evolution is affected by the decisions a planner makes at the beginning of each stage after observing the system state. The decision maker’s goal then is to optimize some measure of system perfor...

This paper investigates the formulation of nonlinear model-predictive control problems with economic objectives on an infinite horizon. The proposed formulation guarantees nominal stability for closed-loop operation. Furthermore, a novel solution method of the infinite horizon method through a transformation of the independent time variable is employed. The closed-loop optimization with infinit...