Description: This paper shows how the results of copula based capital aggregation models can always be locally approximated by relatively simple formulas. The paper defines the concepts of diversification factor and tail correlation matrix and describes methods for estimating these quantities from simulated data. We show how these ideas can be put into practice as both computational shortcuts and presentation tools.

Description: Economic capital is an embedded part of the banking risk management and regulatory framework. The insurance industry has relied on rating agency and regulatory formulas that have been criticized as overcapitalizing and not appropriately differentiating risk drivers in the capital formulation. The emergence of C-3 Phase I and C-3 Phase II have introduced an economic approach to capital in the insurance industry. This half-day seminar takes a detailed look at the subject of economic capital. From the Record of the Society of Actuaries 2005, Volume 31, No. 1: 2005 New Orleans Life Spring Meeting, May 22-24, 2005, Session 9 Seminar.

Description: In this Chapter we present a novel way for estimating aggregated EC figures based on Bayesian copula estimation. Contrary to the classic approach of using a single inter-risk- correlation matrix we derive a probability distribution of possible correlation matrices that enables us to tackle the important issue of parameter uncertainty. Presented at 2010 Enterprise Risk Management Symposium, Society of Actuaries, April 12-15, 2010.

Description: This article discusses the global capital standards for Global Systemically Important Insurers (G-SIIs) and Internationally Active Insurance Groups (IAIGs) currently being developed by the International Association of Insurance Supervisors (IAIS).

Description: This is a concluding and encompassing part of our research on the project entitled \Weighted Premium Calculation Principles and Risk Capital Allocations, which has been supported by the Actuarial Education and Research Fund AERF and the Society of Actuaries Committee on Knowledge Extension Research CKER. We explore the concept of weighted distributions and their role in various phenomena occurring in insurance and finance. In particular, we relate weighted distributions to actuarial and economic premium calculation principles, and also to the capital asset pricing model CAPM. Imitating the latter, we propose a weighted insurance pricing model WIPM. Although general in formulation, we show that the WIPM can successfully be evaluated in a variety of situations, which we illustrate with a number of examples.