This paper presents an optimal portfolio selection approach based on value at risk (VaR), conditional value at risk (CVaR), worst-case value at risk (WVaR) and partitioned value at risk (PVaR) measures as well as calculating these risk measures. Mathematical solution methods for solving these optimization problems are inadequate and very complex for a portfolio with high number of assets. For t...

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...

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...

The worst-possible Value-at-Risk for a non-decreasing function of dependent risks is known when or the copula of the portfolio is bounded from below. In this paper we analyze the properties of the dependence structures leading to this solution, in particular their form and the implied functional dependence between the marginals. Furthermore, we criticise the assumption of the worst-possible sce...

Financial returns exhibit stylized facts such as leptokurtosis, skewness and heavy-tailness. Regarding this behavior, in this paper, we apply multivariate generalized hyperbolic (mGH) distribution for portfolio modeling and performance evaluation, using conditional value at risk (CVaR) as a risk measure and allocating best weights for portfolio selection. Moreover, a robust portfolio optimizati...

Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be evaluated in closed form when only the first two moments are known for the unde...

Assuming absolute continuity of marginals, we give the distribution for sums of dependent random variables from some class of Archimedean copulas and the marginal distribution functions of all order statistics.We use conditional independence structure of random variables from this class of Archimedean copulas and Laplace transform. Additionally, we present an application of our results to VaR e...