This paper addresses a closed-loop supply chain network design problem, in which two different supply chains compete on retail prices by defining a price-dependent demand function. So, the model is formulated in a bi-level stochastic form to demonstrate the Stackelberg competition and associated uncertainties more precisely. Moreover, it is capable of considering random disruptions in the leade...

Stochastic linear quadratic control problems are considered from the viewpoint of risks. In particular, a worst-case conditional value-at-risk (CVaR) objective function is minimized subject to additive disturbances whose first two moments distribution known. The study focuses on three finding optimal feedback gain that minimizes cost of: stationary distribution, one-step, and infinite time hori...

A new approach to optimizing or hedging a portfolio of nancial instruments to reduce risk is presented and tested on applications. It focuses on minimizing Conditional Value-at-Risk (CVaR) rather than minimizing Value-at-Risk (VaR), but portfolios with low CVaR necessarily have low VaR as well. CVaR, also called Mean Excess Loss, Mean Shortfall, or Tail VaR, is anyway considered to be a more co...

C value at risk (CVaR) is both a coherent risk measure and a natural risk statistic. It is often used to measure the risk associated with large losses. In this paper, we study how to estimate the sensitivities of CVaR using Monte Carlo simulation. We first prove that the CVaR sensitivity can be written as a conditional expectation for general loss distributions. We then propose an estimator of ...