While modern portfolio theory grounds on the trade-off between portfolio return and portfolio variance to determine the optimal investment decision, postmodern portfolio theory uses downside risk measures instead of the variance. Prominent examples are given by the risk measures Value-at-Risk...

The current subprime crisis has prompted us to look again into the nature of risk at the tail of the distribution. In particular, we investigate the risk contribution of an asset, which has infrequent but huge losses, to a portfolio using two risk measures, namely Value-at-Risk (VaR) and...

Credit risk is the most important type of risk in terms of monetary value. Another key risk measure is market risk, which is concerned with stocks and bonds, and related financial derivatives, as well as exchange rates and interest rates. This paper is concerned with market risk management and...

We consider a liquidation problem in which a risk-averse trader tries to liquidate a fixed quantity of an asset in the presence of market impact and random price fluctuations. When deciding the liquidation strategy, the trader encounters a trade-off between the transaction costs incurred due to...

Risk driver contributions are key to understanding portfolio risk. Often, this is done by decomposing portfolio ‘volatility’. This is problematic in the presence of non-elliptical distributions. Some asset managers propose switching to value-at-risk (VaR) or expected shortfall (ES) as risk...

We define and develop an approach for risk budgeting allocation -- a risk diversification portfolio strategy -- where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and...

Choosing the appropriate risk criterion has always been one of the main challenges for financial and economic analysts. The goal of this research is to optimize the average portfolio using a multi-layer neural network. In this research, a new model of multilayer neural network has been...

Over the last decade, institutional investors have posted some of the best long-term returns on record. Is it wise for investors to extrapolate these gains into the future, or is now a good time to consider downside protection? In this paper we analyze the current market risks and how tail risk...

Stock investment is one option of investment choice with risks. Investors can reduce their risk by combining several stocks and then forming a portfolio. One method to form an optimal portfolio is by using the Constant Correlation Model (CCM) method. The CCM method focuses on the correlation...

Under the Basel II Accord, banks and other Authorized Deposit-taking Institutions (ADIs) have to communicate their daily risk estimates to the monetary authorities at the beginning of the trading day, using a variety of Value-at-Risk (VaR) models to measure risk. Sometimes the risk estimates...