The aim of this manuscript is to review some results related to portfolio optimization. The models we consider ranges from general semimartingale models to models driven by Itô processes, as well as model driven by Lévy processes. Two optimization problems are studied: the maximization of the utility coming from the final wealth, and the minimization of “shortfall risk” in replicating a conting...

We investigate the computability of problems in probabilistic planning and partially observable innnite-horizon Markov decision processes. The undecidability of the string-existence problem for probabilistic nite automata is adapted to show that the following problem of plan existence in probabilistic planning is undecidable: given a probabilistic planning problem, determine whether there exist...

Relative effects of Beef Quality Assurance (BQA)-related defects in market beef and dairy cows and bulls on selling price at auction was evaluated during 2008. The presence and severity of 23 BQA-related traits were determined during sales in Idaho, California, and Utah. Overall, 18,949 unique lots consisting of 23,479 animals were assessed during 125 dairy sales and 79 beef sales. Mean sale pr...

We investigate the computability of problems in probabilistic planning and partially observable innnite-horizon Markov decision processes. The undecidability of the string-existence problem for probabilistic nite automata is adapted to show that the following problem of plan existence in probabilistic planning is undecidable: given a probabilistic planning problem, determine whether there exist...

Plug-in hybrid electric vehicles (PHEVs) enable their drivers to choose whether to use electricity or gasoline, but this fuel flexibility benefit requires the purchase of additional battery capacity relative to most other vehicles. We value the fuel flexibility of PHEVs by representing the purchase of the battery as the purchase of a strip of call options on the price of transportation. We use ...

For general state and action space Markov decision processes, we present sufficient conditions for the existence of solutions of the average cost optimality inequalities. These conditions also imply the convergence of both the optimal discounted cost value function and policies to the corresponding objects for the average costs per unit time case. Inventory models are natural applications of ou...

We formulate the problem of scheduling a single server in a multi-class queue-ing system as a Markov decision process under the discounted cost and the average cost criteria. We develop a new implementation of the modiied policy iteration (MPI) dynamic programming algorithm to eeciently solve problems with large state spaces and small action spaces. This implementation has an enhanced policy ev...

• We often approximate a large number of periods, even if the horizon is known and finite, by assuming an infinite number of periods, and hope that this assumption will simplify the solution. Indeed, even if the general theory becomes more involved, the solution obtained often is simpler and has important computational and conceptual advantages: in particular, the optimal policy is often statio...