This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without...

This note extends the existing literature on speculative bubbles by allowing for arbitrary trading sequences. As our main result we prove that bubbles may exist in a myopic rational expectations equilibrium (Radner 1979) if and only if every agent expects infinitely many trading opportunities to...

This paper discusses some points of the algebraic optimisation method and the cost comparisons optimisation method. Moreover, mathematical expressions are derived for the backorders level for the EOQ and EPQ inventory models with planned backorders that were not provided by the cost comparisons...

Summary Though there is a huge variety of different Tchebycheff-type inequalities in the literature a systematised structuring is missing. The few existing surveys remain rather enumerative. Therefore in this paper a structuring of Tchebycheff-type inequalities is suggested which is based on...

In winner-take-all tournaments, agents' performance is determined jointly by effort and luck, and the top performer is rewarded. We study the impact of the ''shape of luck'' -- the details of the distribution of performance shocks -- on incentives in such settings. We are concerned with the...