Life insurance decisions under recursive utility

In this paper, we generalize recursive utility to include lifetime uncertainty and utility from bequest. The generalization applies to discrete-time as well as continuous-time recursive utility, and it is an important step forward in the development of recursive utility. We formalize the problem of optimal consumption, investment, and life insurance choice under recursive utility, and we state a verification theorem with a generalized Hamilton-Jacobi-Bellman equation. Our generalization of recursive utility allows us to study optimal consumption, investment, and life insurance choice under separation of (market) risk aversion, elasticity of inter-temporal substitution, and elasticity of substitution between bequest and future utility. The separation gives rise to hump-shaped consumption patterns as observed in realized consumption.     

Smooth investment

In the classical portfolio optimization problem considered by Merton, the resulting constant proportion investment plan requires a diffusive trading strategy. This means that, within any arbitrarily small time interval, the investor must impractically both buy and sell stocks. We study the problems of a mean-square and a power utility investor for whom the trading strategy is constrained to be smooth, i.e. nondiffusive. This means that over sufficiently small time intervals, the investor is either a seller or a buyer of stocks. The mathematical framework is built around quadratic objectives such that trading activity is punished quadratically. Mean-square utility is quadratic, and power utility is covered by quadratic punishment of distance to Merton’s power utility portfolio. We present semi-explicit solutions and, in a series of numerical illustrations, show the impact of trading constraints on the portfolio decision over the investment horizon.     

Note on a new method of construction of mortality tables when the number of lives exposed to risk is unknown

Abstract

It has been known for some time that the d^bx column in a mortality table can be considered as a compound frequency curve with a limited number of maxima and minima. From a theoretical point of view this is of course a self evident conclusion which follows directly from the so-called genetic theory of frequency originally introduced by Laplace. He showed that any frequency distribution can be considered or generated as the sum of a very large number of elementary errors, referrable to several sources of error, each group or error having its own peculiar law of error. While the pure theory of the generation of frequency curves from such secondary sources of elementary errors is simple enough, the inverse and essentially practical problem of decomposing a compound frequency curve into its component or constituent elements is by no means simple and often presents great difficulties, especially if certain restrictions are imposed upon the component curves. An example of such restrictions would be the requirement that all the component curves should be normal Laplacean probability curves.     

The Fear of Exclusion: Individual Effort when Group Formation is Endogenous*

To secure their membership in a popular group, individuals may contribute more to the group's local public good than they would if group formation were exogenous. Those in the most unpopular group do not have this incentive to contribute. This may result in substantial differences in individual effort level between groups. Our model thus provides one explanation for the existence of group‐specific behavioral norms. A principal will prefer exogenous or endogenous group formation depending on whether he prefers high or low levels of the local public good. We analyze two stylized examples: social interaction in schools, and multiple‐task teamwork.     

Attracting responsible employees: Green production as labor market screening

Corporate social responsibility can improve firms’ ability to recruit highly motivated employees. This can secure socially responsible firms’ survival even in a highly competitive environment. We show that if both socially responsible (green) and non-responsible (brown) firms exist in equilibrium, workers with high moral motivation, who shirk less than others, will self-select into the green firms. If unobservable effort is sufficiently important for firm productivity, this can drive every brown firm out of business—even in the case where many workers have no moral motivation whatsoever.     

The distinction between commercial and non-commercial bus services in Germany: Given by nature?

German public transport services by bus are characterized by a regulatory framework that distinguishes between commercial and non-commercial services. Contrary to the apparent views of legislators, this paper shows that costs and revenues are not the only parameters determining whether or not operators are able to provide services in a commercially viable way.Apart from the local characteristics of the specific service, we show that the classification of services as commercial versus non-commercial is determined in large part by the public transport authorities that set minimum quality standards to be provided by operators. Our analysis shows that the authorities awarding the contracts in some cases affect market organization significantly depending on how they make use of this power. Furthermore, market organization differs substantially with respect to the awarding structure and the contractual relationships, thus creating a challenge for operators and authorities in an embryonic market.