The concept of Conditional Value-at-Risk (CVaR) is used in various applications in uncertain environment. This paper introduces CVaR norm for a random variable, which is by de nition CVaR of absolute value of this random variable. It is proved that CVaR norm is indeed a norm in the space of random variables. CVaR norm is de ned in two variations: scaled and non-scaled. L-1 and L-in nity norms a...

The impact of model risk when hedging equity-linked products and other investment guarantees is significant. We propose a to determine the worst-case value an product through partial hedging. Risk control strategies based on conditional Value at measures are used. integrates both mortality financial associated with these find value. adopt robust optimization techniques compute optimal strategy....

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 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...

Following the seminal work by Markowitz, the portfolio selection problem is usually modeled as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model, the risk is measured with variance. Several other risk measures have been later considered thus creating the entire family of mean-risk (Markowitz type) ...

This article develops a safetyanalysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sublevel sets solution nonstandard optimal control problem, where random maximum cost assessed via Conditional V...

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 − α) ∗ 100% drawdowns. The CDD m...