Exploring Exotic Probability Theory

Inspired by the concept of ‘half of a coin’ initiated by Szekely (2005), probabilities can be extended beyond the scope of the Kolmogorov probability axioms where probabilities are always non-negative real numbers. This project will explore exotic probability theory further by examining complex probabilities based on simple scenarios. Following that, the corresponding distributional properties for simple discrete distributions can be derived after introducing the aforementioned theories. This project will also study how simulations can be performed given the distributional properties. Finally, it is important that these newly defined axioms on complex probabilities are consistent with the classical framework of non-negative real probabilities as a special case.

Ashley (Yannan) Lin

Macquarie University

Ashley Lin is currently a student at Macquarie University undertaking a Bachelor of Actuarial Studies. Her interests lie in exotic probability theories and how to apply mathematical and statistical analyses to solve real-world actuarial problems. She is working on this research program to further strengthen her statistical understanding which will benefit her long-term goal of becoming a fully qualified actuary. Outside the classroom, she enjoys participating in various voluntary activities, such as being the Careers Director at Actuarial Students’ Society and providing innovative solutions as a consultant at 180 Degrees Consulting. Also, as a former competitive swimmer, swimming is now her favourite sport to relax and destress.

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