The Phi-martingale

In this paper we focus on continuous martingales evolving in the unit interval $[0,1]$. We first review some results about the martingale property of solution to one-dimensional driftless stochastic differential equations. We then provide a simple way to construct and handle such processes. One of these martingales proves to be analytically tractable, and received the specific name of $Phi$-martingale. It is shown that up to shifting and rescaling constants, it is the only martingale (with the trivial constant, Brownian motion and Geometric Brownian motion) having a separable coefficient $sigma(t,x)=g(t)h(x)$ that can be obtained via a time-homogeneous mapping of Gaussian processes. The approach is applied to the modeling of stochastic survival probabilities

Catastrophe Risk Financing in the United States and the European Union: A Comparative Analysis of Alternative Regulatory Approaches

The regulation of insurance companies in the United States and the European Union (EU) continues to evolve in response to market forces and the changing nature of risk but with somewhat different philosophies and at different rates. One important area where both economic realities and markets are changing is catastrophe risk and its financing. This article examines and compares regulatory and other government policies in the United States and the EU generally and their approaches to the financing of catastrophe risk specifically. It is important to understand the fundamental differences between the two systems to gain insights into their disparate treatment of catastrophe risk financing. Although policies could be improved in both jurisdictions, we argue that the much greater reform is needed in the United States relative to the EU regulatory policies that are being developed. We offer recommendations on how U.S. policies could be significantly improved as well as comment on issues facing the EU. We conclude with some observations on the needs for further progress in the U.S. and EU regulatory systems. Copyright (c) The Journal of Risk and Insurance, 2009.

The Search for an International Accounting Standard for Insurance: Report to the Accountancy Task Force of the Geneva Association

This paper seeks to provide an understanding of the background to the search for an international standard for insurance contracts, which was initiated by the International Accounting Standards Committee (IASC) in 1997 and is still proceeding under its successor, the International Accounting Standard Board (IASB). To do this the paper traces the evolution of the fair value initiative of the IASC/IASB which at the outset was envisaged for all financial instruments, but over time has been amended as the standard setters realized that there would be major problems of implementation, after listening to the views of preparers, particularly the commercial banks, and users, including financial services regulators. The paper identifies the origins of the fair value framework as emanating from an earlier accounting framework based on current values that was intended to be applied generally to all enterprises. The current value initiative, although conceptually sound, has only been adopted in part, again because of problems of implementation. The theoretical underpinning of the current value and fair value accounting approaches are discussed. The paper attempts to show why any early resolution to the insurance contracts project has proved so difficult. This difficulty is evidenced by the fact that insurance contracts have been excluded from the scope of the accounting standard for financial instruments in the United States, FAS 133, as it was clearly recognized that there is no ready market to trade and hence determine fair values for insurance contracts. It concludes by addressing some general factors that must be kept in focus when developing an international accounting standard and some particular factors that should be considered if there is to be a workable and transparent system of financial reporting which captures the economic substance of the commercial operations of insurance companies. Part of the suggested solution is to integrate the insurance contract project more into the revised proposed standard for all financial instruments, IAS 39, and for the IASB to work more closely with insurance companies, especially with their in-house accountants and actuaries. This greater co-operation is now possible as the project moves into the field testing stage. The Geneva Papers on Risk and Insurance (2003) 28, 151–175. doi:10.1111/1468-0440.00215