Conditional Value-at-Risk (CVaR) is a portfolio evaluation function having appealing features such as sub-additivity and convexity. Although the CVaR function is nondifferentiable, scenario-based CVaR minimization problems can be reformulated as linear programs (LPs) that afford solutions via widely-used commercial softwares. However, finding solutions through LP formulations for problems havin...

We compare capital requirements derived by tail conditional expectation (TCE) with those derived by tail conditional median (TCM) and find that there is no clear-cut relationship between these two measures in empirical data. Our results highlight the relevance of TCM as a robust alternative to TCE, especially for regulatory control.

The paper focuses on multi-period aspects of risk functionals. It discusses properties, provides dual representations and offers methods for constructing multiperiod risk functionals. On the way, existence results and representations for conditional risk mappings are derived. In particular, conditional, multi-period and nested versions of the average value-at-risk are given. Finally, the import...

This work investigates the design of risk-perception-aware motion-planning strategies that incorporate non-rational risk associated with uncertain spatial costs. Our proposed method employs Cumulative Prospect Theory (CPT) to generate a perceived map over given environment. CPT-like risks and path-length metrics are then combined define cost function is compliant requirements asymptotic optimal...

With the view of risks, this paper deals with problems maximum hands-off control which aims at minimizing length nonzero input. More specifically, we consider stochastic systems and seek sparse inputs that bring system state to a ball centered origin, such expected value states are further than given threshold from origin is small, thus risk outside ball. To deal problem, employ worst-case Cond...

Electric vehicle (EV) aggregator, as an agent between the electricity market and EV owners, participates in the future and pool market to supply EVs’ requirement. Because of the uncertain nature of pool prices and EVs’ behaviour, this paper proposed a two-stage scenario-based model to obtain optimal decision making of an EV aggregator. To deal with mentioned uncertainties, the aggregator’s risk...

Declaring a benchmark for a manager allows to better define the risk profile of the fund and to evaluate the relative performance against the market (Jorion (2003)). The issue of attracting potential investors in a period of financial crisis and economic recession arise the challenge of designing products which are capable of attracting the interest of investors and highlights the need for clea...

The risk-based assessment is a new approach to the voltage stability assessment in power systems. Under several uncertainties, the security risk of static voltage stability with the consideration of wind power can be evaluated. In this paper, we first build a probabilistic forecast model for wind power generation based on real historical data. Furthermore, we propose a new probability voltage s...