Statistical applications in actuarial science: From cryptocurrency to meme stocks to crop insurance
Date
2022-12
Authors
Stuart, Matthew
Major Professor
Advisor
Yu, Cindy L
Caragea, Petruta C
Wu, Huaiqing
Zhu, Zhengyuan
Kaiser, Mark S
Committee Member
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Abstract
Within this dissertation are three statistical applications to problems in actuarial science. We expand upon the previously established stochastic volatility with discontinuous jumps for financial assets by modeling the sizes of the discontinuous jumps in returns via the asymmetric Laplace distribution (ALD). We also further the new research by proposing bivariate ALD jumps in returns in a 2-d dataset, specifically on a market index and cryptocurrency. We theorize that our findings from the 2-d dataset analysis that cryptocurrencies are considered to be highly speculative in nature. We verify this finding by applying our bivariate ALD model to a 2-d dataset featuring a market index and another financial asset that is also considered highly speculative. Finally, we propose to use semi-parametric quantile regression (SQR) with penalized B-splines to obtain samples from the joint distribution of harvest price and county-level yield for corn and soybean crops, conditioning on the amount of leftover yield from the previous year that is stored for future use, known as stocks. These samples are then used to calculate a Monte Carlo approximation of the county-level insurance premium, and we compare this value to the county-level premiums using samples calculated from the joint distribution of price and yield not conditioned on stocks.
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dissertation