We study the discrete optimization problem under the distributionally robustframework. We optimize the Entropic Value-at-Risk, which is a coherentrisk measure and is also known as Bernstein approximation for the chanceconstraint. We propose an efficient approximation algorithm to resolve theproblem via solving a sequence of nominal problems. The computationalresults show...

Colored potatoes (Solanum tuberosum L.) provide a natural source of phytochemicals that help reduce the risk of diseases. However, there is a lack of information on the degree of variation of the antioxidant activity and polyphenolic contents of these native potatoes. Thus, the antioxidant activity (AA) and total phenolic content (TPC) of native Chilean potatoes were determined. Twelve potato l...

Taxus chinensis var. mairei is an endemic, endangered and first-class protected tree species with great medicinal values in China. Its forest distributes in very limited region and its area is reducing during the last 30 years. Conservation of this species and its communities is urgent. This study aimed to reveal relationships of T. chinensis var. mairei forests with soil variables and topograp...

Tail conditional expectations refer to the expected values of random variables conditioning on some tail events and are closely related to various coherent risk measures. In the univariate case, the tail conditional expectation is asymptotically proportional to the value-at-risk, a popular risk measure. The focus of this paper is on asymptotic relations between the multivariate tail conditional...

Abstract: In this paper, we consider compositions of conditional risk measures in order to obtain time-consistent dynamic risk measures and determine the solvency capital of a life insurer selling pension liabilities or a pension fund with a single cash-flow at maturity. We first recall the notion of conditional, dynamic and time-consistent risk measures. We link the latter with its iterated pr...

The concept of coherent risk measure was introduced in Artzner et al. (1999). They listed some properties, called axioms of ‘coherence’, that any good risk measure should possess, and studied the (non-)coherence of widely-used risk measure such as Value-atRisk (VaR) and expected shortfall (also known as tail conditional expectation or tail VaR). Kusuoka (2001) introduced two additional axioms c...

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...