Uncertain random variables provide a tool to deal with phenomena in which uncertainty and randomness simultaneously exist. This paper proposes a concept of value-at-risk to quantify the risk of an uncertain random system. In addition, a value-at-risk theorem is proved in order to calculate the value-at-risk, and is applied to series systems, parallel system, k -out-ofn system, standby system, a...

Risk management helps the financial industry to manage and estimate risks that may occur by using risk measures. Financial series data mostly have a heavy tail distribution which causes probability of extreme values occur. To overcome these values, it is necessary apply mathematical model in calculating estimates combined with Extreme Value Theory approach. The Adjusted-TVaR measure modificatio...

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...

K e y w o r d s: Family of Sign RCA Models, Value at Risk, backtesting, loss function.

Steven Morrison Steven [email protected] A common definition of an insurer’s economic capital requirements is based around a 1-year Value at Risk (VaR) metric. This defines capital requirements in terms of some tail percentile (typically the 99.5th percentile) of the market-consistent value of the insurer’s balance sheet in 1 year’s time. The problem of estimating such a metric naturally le...

The new workplace is a key arena for learning in today’s society. The spiraling demand for knowledge in the workplace has increased interest in learning, especially team learning. Team learning can be viewed from multiple perspectives, making it difficult for career and technical educators (CTEs) to know how to prepare students for a team-based work environment, especially one that includes vir...

The waterchestnut (Trapa natans var. japonica Nakai) has been dominating the entire in Lake North Inbanuma, Chiba Prefecture, Japan. In order to investigate the seasonal variation of its surface coverage area, photographic recording of surface areas occupied by waterchestnuts in ten quadrats carried out from a boat every two weeks over a period of two years. In addition, the waterchestnuts were...

The views expressed in this paper are those of the authors and do not necessarily reflect those of the Reserve Bank of Australia. A number of people (both within the Reserve Bank and from other banks) provided useful comments. We are particularly grateful to Phil Lowe, Brian Gray and the bank that provided the data for testing.

We use the conditional distribution and conditional expectation of one random variable given the other one being large to capture the strength of dependence in the tails of a bivariate random vector. We study the tail behavior of the boundary conditional cumulative distribution function (cdf) and two forms of conditional tail expectation (CTE) for various bivariate copula families. In general, ...