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The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk plays an important role in protecting the Australian banking sector against insolvency. We outline the mathematical foundations of regulatory capital for…

The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk implements an asymptotic single risk factor (ASRF) model. Measurements from the ASRF model of the prevailing state of Australia's economy and the level…

We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk+ approach, and as such they formally describe default…

A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…

We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is…

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…

The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing…

On March 4th 2016 the Basel Committee on Banking Supervision published a consultative document where a new methodology, called the Standardized Measurement Approach (SMA), is introduced for computing Operational Risk regulatory capital for…

A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences…

Value-at-Risk (VaR) is an institutional measure of risk favored by financial regulators. VaR may be interpreted as a quantile of future portfolio values conditional on the information available, where the most common quantile used is 95%.…

It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that…

Covered bonds are a specific example of senior secured debt. If the issuer of the bonds defaults the proceeds of the assets in the cover pool are used for their debt service. If in this situation the cover pool proceeds do not suffice for…

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…

Any solvency regime for financial institutions should be aligned with the fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. The first objective leads to consider…

Distortion risk measures are extensively used in finance and insurance applications because of their appealing properties. We present three methods to construct new class of distortion functions and measures. The approach involves the…

In the paper we develop mathematical tools of quantile hedging in incomplete market. Those could be used for two significant applications: o calculating the \textbf{optimal capital requirement imposed by Solvency II} (Directive 2009/138/EC…

Many new models for measuring financial contagion have been presented recently. While these models have not been specified for investment funds directly, there are many similarities that could be explored to extend the models. In this work…

We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities…

In this paper I show how reliable estimates of the Value of a Statistical Life (VSL) can be obtained using cross sectional data using Garen's instrumental variable (IV) approach. The increase in the range confidence intervals due to the IV…