In ‎the ‎portfolio ‎optimization, ‎the ‎goal ‎is ‎to ‎distribute ‎the ‎ fixed capital ‎on a‎ ‎set ‎of‎investment ‎opportunities ‎to ‎maximize ‎return ‎while ‎managing ‎risk. ‎Risk ‎and ‎return ‎are ‎quantiti es ‎that ‎are ‎used ‎as ‎input ‎paramete‎rs ‎for ‎the ‎optimal ‎allocation ‎of ‎the ‎capital ‎in ‎the ‎suggested ‎models. ‎ But ‎these ‎quantities ‎are ‎not ‎known ‎at ‎the ‎time ‎of ‎the ‎...

The conditional value at risk (CVaR) is a popular risk measure which enables risk-averse decision making under uncertainty. We consider maximizing the CVaR of a continuous submodular function, an extension of submodular set functions to a continuous domain. One example application is allocating a continuous amount of energy to each sensor in a network, with the goal of detecting intrusion or co...

A coordinated strategy between wind and reversible hydro units for the mid-term that reduces the imbalance of wind power and improves system efficiency is proposed. A stochastic mixed integer linear model is used, which maximizes the joint profit of wind and hydro energies and Conditional Value at Risk (CVaR), where CVaR is the tool utilized to model risk. The offering strategies studied are: i...

In this paper we address the problem of decision making within a Markov de-cision process (MDP) framework where risk and modeling errors are taken intoaccount. Our approach is to minimize a risk-sensitive conditional-value-at-risk(CVaR) objective, as opposed to a standard risk-neutral expectation. We refer tosuch problem as CVaR MDP. Our first contribution is to show that a CVaR...

From the mathematical perspective considered in this tutorial, risk management is a procedure for shaping a risk distribution. Popular functions managing risk are valueat-risk (VaR) and conditional value-at-risk (CVaR). The problem of choice between VaR and CVaR, especially in financial risk management, has been quite popular in academic literature. Reasons affecting the choice between VaR and ...

Enforcing safety in the presence of stochastic uncertainty is a challenging problem. Traditionally, researchers have proposed statistical mean as measure for systems subject to uncertainty. However, ensuring only reasonable if system's safe behavior large number runs interest, which precludes use practical scenarios. In this letter, we propose risk sensitive notion called conditional-value-at-r...