In this thesis, I explore Isaacson’s thesis and Wilkie’s theorem, providing philosophical and formal results on how they relate to each other. At a first approximation, Isaacson’s thesis claims that Peano arithmetic is sound and complete with respect to genuinely arithmetical statements. Using internalist notions familiar from recent work on internal categoricity theorems, I provide a formal de...

1 Drawing borders Logic arose in Antiquity from two sources: the study of real argumentation in the dialectical tradition, and that of axiom-based proof patterns organizing scientific inquiry. Over the centuries that followed, the discipline turned abstract and eventually, profoundly mathematical. Is logic still about human reasoning? Or is it, as Kant and Bolzano said, about an abstraction in ...

We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a spec...

We discuss the data available for the TSE 300 and S&P 500 total return indexes. We consider a number of models, including the Wilkie model and regime switching models. We discuss calibration by maximum likelihood and by Markov chain Monte Carlo for the regime switching lognormal model. We then show how to use this model to price and hedge simple segregated fund maturity guarantees. keywords: Re...

We study a model of common value auctions in which bidders’ private information are independently and asymmetrically distributed. We provide two sufficient conditions under which a first-price auction generates higher revenue than a second-price auction (for a selected equilibrium). A necessary condition is given for this revenue-ranking result to hold in general. We illustrate that in a first-...

Financial literacy and cognitive capabilities are convincingly linked to the quality of financial decision-making, influencing savings, stock-picking, and avoidance of outright financial mistakes. Yet, there is little evidence that education intended to improve financial decision-making is successful. Using plausibly exogenous variation in exposure to state-mandated personal finance and mathema...

Duration of an event tends to be underestimated as it becomes temporally distant (Spetch & Wilkie, 1983). The current study investigated this so-called choose-short effect in time and length in order to reevaluate the claim that the choose-short effect is special to temporal memory (Wearden, Parry, & Stamp, 2002). Participants made discrimination judgments in time or length on a pair of line st...

In the absence of investment and dividend payments, the surplus is modeled by a Brownian motion. But now assume that the surplus earns investment income at a constant rate of credit interest. Dividends are paid to the shareholders according to a barrier strategy. It is shown how the expected discounted value of the dividends and the optimal dividend barrier can be calculated; Kummer’s confluent...

Eliciting Domain Knowledge Using Conceptual Metaphors: A Case Study from Music Interaction Conference Item How to cite: Wilkie, Katie; Holland, Simon and Mulholland, Paul (2014). Eliciting Domain Knowledge Using Conceptual Metaphors: A Case Study from Music Interaction. In: Proceedings of the 28th International BCS Human Computer Interaction Conference (HCI 2014), Sept 9 12, 2014, Southport, UK...

Tree JJ and Wilkie J. Face and object imagery in congenital prosopagnosia: A case series.