We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equa...

The problem of allocation of orders for parts among part suppliers in a customer driven supply chain with operational risk is formulated as a stochastic singleor bi-objective mixed integer program. Given a set of customer orders for products, the decision maker needs to decide fromwhich supplier to purchase parts required for each customer order to minimize total cost and to mitigate the impact...

Suppose X1, · · · , Xn are random variables with the same known marginal distribution F but unknown dependence structure. In this paper, we study the smallest possible value of P(X1 + · · ·+ Xn < s) over all possible dependence structures, denoted by mn,F(s). We show that mn,F(ns) → 0 for s no more than the mean of F under weak assumptions. We also derive a limit of mn,F(ns) for any s ∈ R with ...

We suggest a new methodology to overcome several well-known deeciencies of Value at Risk computations. Our approach mainly addresses two aspects of Value at Risk: rst, to avoid potentially disastrous clustering in predicted tail events we derive a new approach to accurately estimating the conditional distribution of asset returns using maximum entropy densities. Second, by the very nature of th...

design of a logistics network in proper way provides a proper platform for efficient and effective supply chain management. this paper studies a multi-period, multi echelon and multi-product integrated forward-reverse logistics network under uncertainty. first, an efficient complex mixed-integer linear programming (milp) model by considering some real-world assumptions is developed for the inte...

Portfolio optimization problems involving Value-at-Risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfoli...

The theory of risk provides a systematic approach to handling uncertainty with well-defined risk and deviation measures. As the model-based economic optimization of the water-flooding process in oil reservoirs suffers from high levels of uncertainty, the concepts from the theory of risk are highly relevant. In this paper, the main focus is to offer an asymmetric risk management, i.e., to maximi...

This paper introduces the notions of stability, ultimate boundedness, and positive invariance for stochastic systems in view risk. More specifically, those are defined terms worst-case Conditional Value-at-Risk (CVaR), which quantifies conditional expectation losses exceeding a certain threshold over set possible uncertainties. Those allow us to focus our attention on tail behavior analysis dyn...