Optimal hedging of demographic risk in life insurance

A Markov chain model is taken to describe the development of a multi-state life insurance policy or portfolio in a stochastic economic?Cdemographic environment. It is assumed that there exists an arbitrage-free market with tradeable securities derived from demographic indices. Adopting a mean-variance criterion, two problems are formulated and solved. First, how can an insurer optimally hedge environmental risk by trading in a given set of derivatives? Second, assuming that insurers perform optimal hedging strategies in a given derivatives market, how can the very derivatives be designed in order to minimize the average hedging error across a given population of insurers? The paper comes with the caveat emptor that the theory will find its prime applications, not in securitization of longevity risk, but rather in securitization of catastrophic mortality risk.     

On the inversion of a moving average

Abstract

At the request of the Faculty of Science of Stockholms Högskola I had the pleasure to act as opponent at the doctoral discussion on Mr. HERMAN WOLD?s dissertation: »A Study in the Analysis of Stationary Time Series». Both the reading of the book, the public discussion and a subsequent private correspondance with the author, I have found very interesting and stimulating. I have also had the pleasure to discuss to some extent this matter with Professor CRAMÉR. Some of the points raised during our exchanging of views have been covered by Mr. Wold in his note in this issue of the »Aktuarietidskrift», but not all. It may therefore be worth while to add a few remarks. I need not dwell upon the various merits of the book, they speak for themselves. Here, I shall confine myself to one particular point where some difference of opinion still seems to persist, namely the significance of the formula (255) in the dissertation, which is the same as (13) in Mr. WOLD? note in this issue. This formula is intended as an inversion formula for a moving average on a random variable in the singular case where the characteristic equation of the moving average has at least one root on the unit circle.     

Solution d'un problème du calcul des probabilités

Abstract

A la dernière réunion annuelle de la Société Norvégienne de Mathématiques, M. le Professeur Guldberg a fait une conférence très intéressante, dans laquelle il a montré comment on est arrivé par des considérations élémentaires du calcul des probabilités à un problème connu sous le nom de “Problème de Simmons”. Je me permets de présenter quelques réflexions sur ce problème, que m'a suggéré l'intéressante conférence de M. Guldberg.     

Magisterkonferens i Forsikringsmatematik ved Københavns Universitet 1922–23. Den skriftlige Prøve.

Abstract

A. Purpose of this note

Any specific application of the theory in Section 3 of the paper would demand that the statewise reserves V_j be precisely defined. There is some latitude at this point, however, and it turns out that Theorem 3 as stated may require that an appropriate definition be used. Paragraph B of the present note adds rigour on the issue. Paragraph C offers some guidance as to how to construct and compute the reserves in nontrivial cases. Some technical lemmas are placed in the final Paragraph D.     

Econometric Evaluation of the New Keynesian Phillips Curve*

We give an appraisal of the New Keynesian Phillips curve (NPCM) as an empirical model of European inflation. The favourable evidence for NPCMs on euro‐area data reported in earlier studies is shown to depend on specific choices made about estimation methodology. The NPCM can be re‐interpreted as a highly restricted equilibrium correction model. We also report the outcome of tests based on variable addition and encompassing of existing models. The results show that economists should not accept the NPCM too readily.     

Loss of economic rents in the global fishery

Most of the world’s ocean fisheries are severely lacking in private property rights in the underlying natural resources or their close complements (e.g. harvesting volume). Therefore, according to standard property rights theory, these fisheries should be highly wasteful of potential economic rents from these resources. The question is whether this economic loss can be empirically verified and, if so, how large it is. This paper explains the concept and develops the analytical theory of economic and natural rents. Building on this and utilizing global fisheries data, the paper proceeds to estimate a global fisheries model, obtain numerical estimates of the rent loss in the world’s ocean capture fisheries and provide reasonable confidence bounds for this loss. It is found that the global fisheries rent loss constitutes almost certainly a large fraction of the landed value of the global landings. The mean estimate of this loss is well over 50% of the value of landings.     

Nachruf für Sir Ronald Fisher

Ohne Zusammenfassung