On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

Executive Stock Options: Exercise Policy and Market Reaction

In this paper I investigate the exercise policy, and the market reaction to that, of the executive stock option holders in Finland. The empirical tests are conducted with aggregated firm level data from 34 firms and 41 stock option programs. I find some evidence of an inverse relation between the exercise intensity of the options holders and the future abnormal return of the company share price. This finding is supported by the view that information about future company prospect seems to be the only theoretical attribute that could delay the exercise of the options. Moreover, a high concentration of exercises in the beginning of the exercise window is predicted and the market is expected to react to deviations from this. The empirical findings however show that the market does not react homogenously to the information revealed by the late exercises.

Share Repurchases, Dividends, and Executive Options

This paper reports empirical results on the determinants of the authorization decision for share repurchases and dividends in Finland. We use a data set with precise data on share repurchases as well as characteristics for the option programs. Contrary to the U.S., we use a data set where 41% of the options are dividend protected, which allows us to separate between the "option funding" and "substitution / managerial wealth" hypothesis for the choice of the distribution method. We find that foreign ownership is the main determinant for share repurchases in Finland and attribute this relationship to tax factors. We also find evidence in support of both the signaling and agency cost hypotheses for cash distributions, especially in the case of share repurchases. Finally, we find a significant difference between companies with and without dividend protected options. When options are dividend protected, the relationship between dividend distributions and the scope of the options program turns to a significantly positive one instead of the negative one documented on U.S. data. This gives some support for the substitution / managerial wealth hypothesis as a determinant for the choice of the distribution method.