With the increased acceptance of capital market efficiency, there has been a significant increase in the money managed on an indexed basis. Several methodologies are available to replicate the target index. In this paper, we discuss the problems of (1) defining suitable performance objectives...

Value at Risk has lost the battle against Expected Shortfall on theoretical grounds, the latter satisfying all coherence properties while the former may, on carefully constructed cases, lack the sub-additivity property that is in a sense, the most important property a risk measure ought to...

The departure in modelling terms from the log-normal distribution for option pricing has been largely driven by empirical observations on skewness. In recent years, the Weibull and generalized beta distributions have been used to fit the risk-neutral density from option prices. In this article,...

The loss distribution approach is one of the three advanced measurement approaches to the Pillar I modeling proposed by Basel II in 2001. In this paper, one possible approximation of the aggregate and maximum loss distribution in the extremely low frequency/high severity case is given, i.e. the...

Sample covariance is known to be a poor estimate when the data are scarce compared with the dimension. To reduce the estimation error, various structures are usually imposed on the covariance such as low-rank plus diagonal (factor models), banded models and sparse inverse covariances. We...

This paper describes a new technique that can be used in financial mathematics for a wide range of situations where the calculation of complicated integrals is required. The numerical schemes proposed here are deterministic in nature but their proof relies on known results from probability...

The integration of quantitative asset allocation models and the judgment of portfolio managers and analysts (i.e. qualitative view) dates back to a series of papers by Black and Litterman in the early 1990s. In this paper we improve the classical Black-Litterman model by applying more realistic...

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