An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

Raising the Level of Moral Thinking among Managers Will Not Help. Kohlberg's Conventionality and Systemic Ethical Flaws in Business

Business ethicists often assume that unethical behavior arises when individuals deviate from the norms and responsibilities that are institutionalized to frame economic activities. People's greed motivates them to violate the rules of the game. In Kohlberg's terms, it is assumed that such actors make decisions in a preconventional way and act opportunistically. In this article, we propose an alternative interpretation of deviant behavior, arguing that such behavior does not result from a lack of conventional moral guidance but rather from the fact that characteristics attributed to preconventional morality by Kohlberg - the purely incentive and punishment driven opportunistic morality - have become the conventionalized morality. The prevailing norms that economic actors have internalized as their yardstick are those of the preconventional Homo economicus. Not the deviation from, but the compliance with the rules of the game explains many forms of harmful and illegal decisions made in corporations.