Midterm Colloquium Jeroen Mulder

The hyperbolic Fourier transform for Risk analysis

Supervisor: Dr. ir. Max Mendel

This literature review investigates how the trade of risk within economic systems can be modelled using thermodynamic analogies, most notably the analogy between systematic risk and entropy. Currently risk in the economic literature is split into idiosyncratic (diversifiable) and systematic (un-diversifiable) risk. However, this distinction between the two risk types is often simplified by viewing idiosyncratic risk as merely the residuals or by generalizing to one standard deviation.

This research proposes to use split complex numbers and a hyperbolic Fourier transform to develop a new interpretation of risk analysis, modelling and trade. The use Split complex numbers in the mathematical framework of statistical mechanics allows for the analysis of the distinct risk components in a complex Risk spectrum. This captures the hyperbolic behaviour of the risk components as observed in the literature. Allowing for the analysis of risk, within Economic Engineering, by its distinct components.