Assume a representative-agent economy with one good. Let time be indexed by t=0,1,2,.... Suppose that there is no uncertainty at time zero and that S branches stem out of it. Similarly, from each of these branches, S more branches stem out, and so on. For a given t, label the (cross-section of) nodes as {1, ..., St} and note that St increases over time. Our agent’s utility will now be defined o...

This paper presents an explicitly solved model of wealth distribution in an infinite-horizon incomplete-markets economy. The agent aims to hold a target level of wealth in order to partially buffer income shocks. The notion of buffering suggests that the agent’s wealth is less skewed and less fat-tailed than his income in the long run. Infinite-horizon setting implies that the cross-sectional j...

1. These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis. 2. Comments are welcome and may be addressed to :

In this article we consider risk-sensitive control of semi-Markov processes with a discrete state space. We general utility functions and discounted cost in the optimization criteria. random finite horizon infinite problems. Using augmentation technique characterize value also prescribe optimal controls.

We present a memory-bounded approximate algorithm for solving infinite-horizon decentralized partially observable Markov decision processes (DEC-POMDPs). In particular, we improve upon the bounded policy iteration (BPI) approach, which searches for a locally optimal stochastic finite state controller, by accompanying reachability analysis on controller nodes. As a result, the algorithm has diff...

This paper discusses why the selection of a finite planning horizon is preferable to an infinite one for a replenishment policy of production inventory models. In a production inventory model, the production rate is dependent on both the demand rate and the inventory level. When there is an exponentially decreasing demand, the application of an infinite planning horizon model is not suitable. T...

We investigate analytical cost distributions in the setting of a dynamic stochastic scheduling problem where customers are served from a central location within some given time-frame, for the case where customer locations are uniformly distributed on the boundary of the unit circle. Two distance metrics are considered and analytical expressions for the distribution of the resulting costs are de...

Abstrucf-We formulate and solve a dynamic stochastic optimization problem of a nonstandard type, whose optimal solution features active learning. The proof of optimality and the derivation of the corresponding control policies is an indirect one, which relates the original single-person optimization problem to a sequence of nested zero-sum stochastic games. Existence of saddle points for these ...

We address in this paper the challenge of solving a nonhomogeneous infinite horizon Markov Decision Process (MDP) problem. More precisely, we seek an algorithm that, when given a finite subset of the problem’s potentially infinite data set, delivers an optimal first period policy. Such an algorithm can thus recursively generate within a rolling horizon procedure an infinite horizon optimal solu...