Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends

Abstract

In this paper asset and liability values are modeled by geometric Brownian motions. In the first part of the paper we consider a pension plan sponsor with the funding objective that the pension asset value is to be within a band that is proportional to the pension liability value. Whenever the asset value is about to fall below the lower barrier or boundary of the band, the sponsor will provide sufficient funds to prevent this from happening. If, on the other hand, the asset value is about to exceed the upper barrier of the band, the assets are reduced by the potential overflow and returned to the sponsor. This paper calculates the expected present value of the payments to be made by the sponsor as well as that of the refunds to the sponsor. In particular we are interested in situations where these two expected values are equal. In the second part of the paper the refunds at the upper barrier are interpreted as the dividends paid to the shareholders of a company according to a barrier strategy. However, if the (modified) asset value ever falls to the liability value, which is the lower barrier, “ruin” takes place, and no more dividends can be paid. We derive an explicit expression for the expected discounted dividends before ruin. From this we find an explicit expression for the proportionality constant of the upper barrier that maximizes the expected discounted dividends. If the initial asset value is the optimal upper barrier, there is a particularly simple and intriguing expression for the expected discounted dividends, which can be interpreted as the present value of a deterministic perpetuity with exponentially growing payments.     

Co-voting democracy

We outline a new voting procedure for representative democracies. This procedure should be used for important decisions only and consists of two voting rounds: a randomly-selected subset of the citizens is awarded a one-time voting right. The parliament also votes, and the two decisions are weighted according to a pre-defined key. The final decision is implemented. As this procedure gives the society—represented by the randomly-chosen subset—a better say for important decisions, the citizens might be more willing to accept the consequences of these decisions.     

《现代主义之后的艺术史》 9、艺术对抗艺术史——以大众文化为镜

二战结束后,"艺术与生活"这对著名的对质命题即刻成为决定现代主义命运的根本因素,战后现代主义调头驶向战前现代主义的反方向。战后的标语不再是以艺术的名义(也是代设计美术和建筑美学而言)掌控"生活",赋予"生活"以强烈的"风格"。在美国人视线未及的欧洲,人     

Collective Trust Behavior*

This paper investigates trust behavior in situations where decision‐makers are large groups and the decision mechanism is collective. Theories from behavioral economics and psychology suggest that trust in such situations may differ from interindividual trust. The experimental results here reveal a large difference in trust but not in trustworthiness between the individual and collective setting. Furthermore, a field experiment captures the determinants of collective trust behavior among two Swedish cohorts. Beliefs about the other group and one's own group are strongly associated with collective trustworthiness and trust behavior.     

How Will EMU Affect Inflation and Unemployment in Europe?

This paper explores how European Monetary Union will change the wage setting behavior of national labor unions. We derive the impact of national inflation aversion and labor militancy on the performance of national labor markets under different monetary arrangements. A common central bank raises inflation and unemployment if it acts as conservatively as national central banks. However, unemployment falls in countries that previously tied their monetary policy to the Bundesbank. We also examine the composition of EMU and the influence of national labor market legislation.
JEL Classification : E 24; F 02; F 33     

A note on capital asset pricing and heterogeneous taxes

In this paper, we present a stylized model where we show how asset prices, i.e., required expected rates of returns, may be characterized in a world with heterogeneous asset taxes. Within a simple CAPM-like framework, we derive an after-tax beta equal to the pre-tax beta multiplied by a (non-obvious) asset specific tax adjustment. We further show in what sense the Security Market Line here can be replaced by a Security Market Fan. Well-known CAPM relations are obtained as special cases, and policy implications are analyzed.     

Can statisticians beat surgeons at the planning of operations?

The planning of operations in the Academic Medical Center is primarily based on the assessments of the length of the operation by the surgeons. We investigate whether duration models employing the information available at the moment the planning is made, offer a better alternative. Our empirical results indicate that statistical methods often do better than surgeons. This does not imply that the surgeons’ predictions do not contain valuable information. This information is a key explanatory variable in our statistical models. What our conclusion does entail is that a correction of the predictions of surgeons is possible because they are often under- or overestimating the actual length of operations.