Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as i...

In the Lee-Carter framework, future survival probabilities are random variables with an intricate distribution function. In large homogeneous portfolios of life annuities, Value-at-Risk or Conditional Tail Expectation of the total yearly payout of the company are approximately equal to the corresponding quantities involving random survival probabilities. This paper aims to derive some bounds in...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive model for multi-losses whose dependence and tail heaviness are influenced by a heavy-tailed background...

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach co...

In order to protect stakeholders of insurance companies and financial institutions against adverse outcomes of risky businesses, regulators and senior management use capital allocation techniques. For enterprise-wide risk management, it has become important to calculate the contribution of each risk within a portfolio. For that purpose, bivariate lower and upper orthant tail value-at-risk can b...

An acceptability measure is a number that summarizes information on monetary outcomes of a given position in various scenarios, and that, depending on context, may be interpreted as a capital requirement or as a price. In a multiperiod setting, it is reasonable to require that an acceptability measure should satisfy certain conditions of time consistency. Various notions of time consistency may...

Consider a portfolio of n obligors such as loans, corporate bonds and other instruments subject to possible default. Tang and Yuan (2012, Submitted) introduced a new model for the loss given default and studied its tail behavior, Value at Risk, and Conditional Tail Expectation under the assumption that the losses jointly follow a multivariate regularly varying distribution. However, in the case...