In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation...

We set the context for capital approximation within the framework of the Basel II/III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord,...

In this manuscript we explore a range of perspectives being adopted by industry and regulators in order to classify cyber crime or cyber risk loss processes. The purpose of this is to better understand and discuss the emerging perspectives on this class of risk process in order to inform...

A common feature of retirement income products is that their payouts depend on the lifetime of policyholders. A typical example is a life annuity policy which promises to provide benefits regularly as long as the retiree is alive. Consequently, insurers have to rely on "best estimate" life...

This work explores the common attributes of different types of cyber risk with a view to better understanding the key attributes that contribute to each type of cyber risk category. In doing so we explore event studies on a range of different market sectors, different countries, different...

We propose a novel generalization to the Student-t Probabilistic Principal Component methodology which: (1) accounts for an asymmetric distribution of the observation data; (2) is a framework for grouped and generalized multiple-degree-of-freedom structures, which provides a more flexible...

In stochastic multi-factor commodity models, it is often the case that futures prices are explained by two latent state variables which represent the short and long term stochastic factors. In this work, we develop the family of stochastic models using polynomial diffusion to obtain the...

The Schwartz-Smith two-factor model (Schwartz & Smith, 2000) was commonly used in the pricing of commodity futures in the last two decades. In 2016, (Filipovic & Larsson, 2016) introduced a polynomial diffusion framework which allows a more complex struc- ture of spot price. This framework has...

"Co-edited by acknowledged experts in the quantification of operational risk, Handbook of Operational Risk conveniently and systematically displays all of the financial engineering topics, theories, applications, and current statistical methodologies that are intrinsic to the subject matter....