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...

abstract portfolio definition is the most important decision for individuals and legal persons that invest in stock. the main objective of this paper is study and determination of optimal portfolio for stock of active food industrial company in tehran stock based on value at risk (var) index. for this purpose, we used weekly static of stock of active food industrial company in tehran from bahma...

An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-at-Risk (VaR) risk measure. The existing methodo...

Recent literature has investigated the risk aggregation of a portfolio X = (Xi)1≤i≤n under the sole assumption that the marginal distributions of the risks Xi are specified but not their dependence structure. There exists a range of possible values for any risk measure of S = ∑n i=1Xi and the dependence uncertainty spread, as measured by the difference between the upper bound and the lower boun...

A distortion risk measure used in finance and insurance is defined as the expected value of potential loss under a scenario probability measure. In this paper, the tail distortion risk measure is introduced to assess tail risks of excess losses modeled by the right tails of loss distributions. The asymptotic linear relation between tail distortion and Value-at-Risk is derived for heavy tailed l...

In this paper we model Value-at-Risk (VaR) for daily stock index returns using a collection of parametric models of the ARCH family based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, Va...

Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as i...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive model for multi-losses whose dependence and tail heaviness are influenced by a heavy-tailed background...