We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a so-called Partitioned Value-atRisk (PVaR) measure by using half-space statistical information. Using simulated and real data, the PVaR approach generates better risk-return tradeoffs in the optimal portfolios when compared to Markowitz mea...

Risk management through marginal rebalancing is important for institutional investors due to the size of their portfolios. We consider the problem of improving marginally portfolio VaR and CVaR through a marginal change in the portfolio return characteristics. We study the relative significance of standard deviation, mean, tail thickness, and skewness in a parametric setting assuming a Student’...

This paper evaluates the data from the recent financial crisis to examine the risk spillover effects of financial markets value at risk (VaR), which captures the extreme behavior of an asset, is considered a measure of risk in an asset or in a market. We hypothesize that an extreme downside movement of returns in a market measured by a VaR has negative effects on other markets, causing a simila...

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...

Modeling the dependence among multiple loss triangles has important implications for the determination of loss reserves, a critical element of risk management and capital allocation practices of property-casualty insurers. In this article, we propose a copula regression model for dependent lines of business that can be used to predict unpaid losses and hence determine loss reserves. The propose...

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...

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the “average of the 100p% worst losses” in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representations of ES which turn out to be more appropriate for certain purposes.

Gold has been recognized as the most important precious metals in the human society. Other than as a medium of exchange, gold has been a consumption and investment product for a long history. It has been recognized a well-positive role in portfolio performance by many financial market practitioners. During the recent financial crisis, gold spot prices have exhibited significant volatility. Thus...