PhD Defense Johan Auster
Title: Essays in Computational Finance
Abstract: This dissertation contains an assortment of articles pertaining to mathematical finance
and computational methods. A total of four articles are included, covering a wide range of topics detailed below.
The first article covers various methods for the approximation of the exponential function with relevant adjustments specific to implementations using fixed-point numbers, which are of particular relevance in decentralized finance applications, where (the more commonly used) floating-point numbers are typically not available.
The second article demonstrates the utilization of dual numbers in the diffusion operator integral variance reduction method proposed by Heath and Platen. Using dual numbers for exact differentiation allows the method to be extended to complex option pricing problems that have existing solutions in the Black-Scholes model without the need for error-prone derivations of analytical sensitivities. The method is applied to the pricing of discretely-monitored down-and-out call barrier options and floating-strike lookback putoptions.
The third article introduces a generalization of a scalable reward distribution method frequently used in practical implementations of smart contracts. This generalization allows for the constant-time distribution of an arbitrary claims process among accounts according to their (changing) relative shares. Special cases covering deposit-backed claims and delayed allocation are covered, along with a formalization of blockchains, smart contracts and associated filtrations that allows for an interpretation consistent with the
presented continuous-time setup.
The fourth and final article presents a method for identifying the "most equitable" distribution of an integer budget among integer allocations when constraints apply to individual allocations. In a first step, a table characterization of real-valued solutions is constructed, which can be cached (stored) for future use. A second step then retrieves integer allocations that solve the original problem from this characterization. An example application to the allocation of space in graphical user interfaces is then shown.
Supervisor: Professor Rolf Poulsen, Department of Mathematical Sciences
Assessment committee:
Associate Professor, David G. Skovmand (Chair)
Professor Natalie Packham, Berlin School of Economics and Law
Head quant, Artur Sepp, LGT Bank AG, Zurich, Switzerland