Investors use different approaches to select optimal portfolio. so, Optimal investment choices according to return can be interpreted in different models. The traditional approach to allocate portfolio selection called a mean - variance explains. Another approach is Markov chain. Markov chain is a random process without memory. This means that the conditional probability distribution of the nex...

We generalize and build on the PAC Learning framework for Markov Decision Processes developed in Jain and Varaiya (2006). We consider the reward function to depend on both the state and the action. Both the state and action spaces can potentially be countably infinite. We obtain an estimate for the value function of a Markov decision process, which assigns to each policy its expected discounted...

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for oth...

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for oth...

We present X-Bounds, a new tool to implement a methodology based on stochastic ordering, algorithmic derivation of simpler Markov chains and numerical analysis of these chains. The performance indices defined by reward functions are stochastically bounded by reward functions computed on much simpler or smaller Markov chains obtained after aggregation or simplification. This leads to an importan...

Today many formalisms exist for specifying complex Markov chains. In contrast, formalism for specifying the quantitative properties to analyze have remained quite primitive. In this paper a new formalism of temporal rewards that allows complex quantitative properties (including delay type measures) to be expressed in the form of a temporal reward formula. Together, an initial (discrete-time) Ma...

We consider infinite-state discrete Markov chains which are eager: the probability of avoiding a defined set of final states for more than n steps is bounded by some exponentially decreasing function f(n). We prove that eager Markov chains include those induced by Probabilistic Lossy Channel Systems, Probabilistic Vector Addition Systems with States, and Noisy Turing Machines, and that the boun...

We consider manufacturing problems which can be modelled as finite horizon Markov decision processes for which the effective reward function is either a strictly concave or strictly convex functional of the distribution of the final state. Reward structures such as these often arise when penalty factors are incorporated into the usual expected reward objective function. For convex problems ther...

In this paper, we propose a framework to analyze Markov reward models, which are commonly used in system performability analysis. The framework builds on a set of analytical tools developed for a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS). The state space of an SHS is comprised of: i) a discrete state that describes the possible configurations/modes that a syst...