We study the problem of finding the worst-case joint distribution of a set of risk factors given prescribed multivariate marginals with nonlinear loss function. The method has applications to any situation where marginals are provided, and bounds need to be determined on total portfolio risk....

We present a model for P/L insurance companies based on Asset-Liability-Management (ALM). We show analytically for multivariate normal distributed assets and claims that an overall minimum of the required risk capital can be obtained by refining the firm's asset allocation when including a ruin...

This note highlights the impact of changing the aggregation currency when testing for capital adequacy. This is exemplified using the two most prominent capital adequacy tests used in the financial industry: Value-at-Risk and Expected Shortfall. The test consists in establishing whether the...

Despite the use of VaR as a means to control risk, using VaR can have the opposite effect. VaR is used by bank and insurance regulators more than any other risk measure. A value-at-risk (VaR) constraint on the probability that future firm equity value will be less than a floor, when the floor is...

We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a...

We study capital requirements for bounded financial positions defined as the minimum amount of capital to invest in a chosen eligible asset targeting a pre-specified acceptability test. We allow for general acceptance sets and general eligible assets, including defaultable bonds. Since the...

With a sample of twelve US bond indices spanning different maturities, credit ratings and industry sectors, we investigate the impact of new bank capital regulation for trading portfolios introduced by Basel III. Specifically, we estimate the new capital requirements for (a) liquidity risk and...

In this paper, we study an optimal investment problem under joint initial-time and intermediate-time Value-at-Risk regulations and a portfolio insurance (PI) constraint on terminal wealth faced by a defined-contribution pension fund manager. The objective is to maximize the expected utility from...

In modern frameworks for financial regulation such as Basel III, IV as well as Solvency II, financial institutions are regulated to maintain a certain level of capital to prepare for potential future losses. In this paper, we take the perspective of a regulator who designs regulatory capital...