Realizability Toposes from Specifications

We investigate a framework of Krivine realizability with I/O effects, and present a method of associating realizability models to specifications on the I/O behavior of processes, by using adequate interpretations of the central concepts of `pole' and `proof-like term'. This method does in particular allow to associate realizability models to computable functions. Following recent work of Streicher and others we show how these models give rise to triposes and toposes

A 2-Categorical Analysis of the Tripos-to-Topos Construction

We characterize the tripos-to-topos construction of Hyland, Johnstone and Pitts as a biadjunction in a bicategory enriched category of equipment-like structures. These abstract concepts are necessary to handle the presence of oplax constructs --- the construction is only oplax functorial on certain classes of cartesian functors between triposes. A by-product of our analysis is the decomposition of the tripos-to-topos construction into two steps, the intermediate step being a weakened version of quasitoposes

Evolutionary and Population Dynamics: A Coupled Approach

We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by population dynamics in general. Especially for fast reproducing microbes which are subject to selection, both types of dynamics are often closely intertwined. We illustrate this by considering different growth scenarios. Depending on whether microbes die or stop to reproduce (dormancy), qualitatively different behaviors emerge. For cooperating bacteria, a permanent increase of costly cooperation can occur. Even if not permanent, cooperation can still increase transiently due to demographic fluctuations. We validate our analysis via stochastic simulations and analytic calculations. In particular, we derive a condition for an increase in the level of cooperation.Comment: 12 pages, 5 figure

Impredicative Encodings of (Higher) Inductive Types

Postulating an impredicative universe in dependent type theory allows System F style encodings of finitary inductive types, but these fail to satisfy the relevant {\eta}-equalities and consequently do not admit dependent eliminators. To recover {\eta} and dependent elimination, we present a method to construct refinements of these impredicative encodings, using ideas from homotopy type theory. We then extend our method to construct impredicative encodings of some higher inductive types, such as 1-truncation and the unit circle S1

Classical realizability in the CPS target language

AbstractMotivated by considerations about Krivine's classical realizability, we introduce a term calculus for an intuitionistic logic with record types, which we call the CPS target language. We give a reformulation of the constructions of classical realizability in this language, using the categorical techniques of realizability triposes and toposes.We argue that the presentation of classical realizability in the CPS target language simplifies calculations in realizability toposes, in particular it admits a nice presentation of conjunction as intersection type which is inspired by Girard's ludics

Essays in behavioural finance

This thesis studies the role of contrast effects and biased expectations in financial decisionmaking and financial markets. The first study explores the role of skewness preferences in dynamic decision-making at the hands of salience theory. Previous research suggests that otherwise risk-averse people are willing to take risks if the outcome distribution is positively skewed. Salience theory can explain this by assuming that states with high contrasts between the outcomes attract attention and their probability is overestimated. Skewness preferences are particularly important in dynamic setups because these allow agents to endogenously create skewness through the choice of their stopping strategy. I extend salience theory to a dynamic setup and show that it predicts that agents will take gambles if the expected value is not too negative. Moreover, if they gamble they choose stopping strategies that yield positively skewed outcome distributions. These predictions differ both from expected utility theory and other behavioural models. I test the predictions experimentally and find broad support. In the second study, I examine whether the earnings forecasts of analysts after a firm announces its earnings depend on the earnings surprises of companies that announced shortly before the firm. Evidence from a plethora of domains suggests that the interpretation of information depends on how it compares to contrasting information. Thus, the earnings of a given firm might look worse the better other firms perform. I find that positive earnings surprises of other firms make analysts revise their forecast of a firm’s earnings upwards but, at the same time, make their forecast more pessimistic relative to the true earnings. This result is in line with a positive news channel in combination with a contrast effect channel of the other firms’ earnings surprise on the analysts’ forecasts. In the third study, I develop a method to test if a given return predictor reflects mispricing rather than risk. Asset pricing research has uncovered hundreds of characteristics that can predict the cross-section of returns, but the nature of many of these remains elusive. If a predictor is linked to returns through risk, it should be unrelated to changes in the market’s expectations about firm profits. Alternatively, return predictably can be explained by biased expectations. If a return predictor captures this form of mispricing, it should predict changes in expectations in addition to returns. I use the earnings forecasts of professional analysts as a proxy to the market’s expectations and test for 173 return predictors if they can also predict forecast revisions. I find that around 40% of predictors can do so and, thus, reflect mispricing