Actuarial studies seminar - Professor Ken Sui - Macquarie University

A seminar by Professor Ken Sui from Macquarie University

Title: Bayesian Nonlinear Expectation and Its Applications

Abstract: Bayesian statistics and nonlinear expectation provide two important approaches to incorporate model uncertainty or ambiguity. While historical developments of the two approaches may have some divergences, it may be intriguing to explore possibilities of bridging the two approaches. As an endeavor to build this bridge, Bayesian nonlinear expectation is introduced through applications of two versions of the Bayes rule. One version is used to evaluate posterior distributions for uncertain parameters and their credible intervals, and the other version is adopted to introduce a set of alternative probability models through Girsanov-type change of probability measures in discrete time. In this talk, we shall discuss the notion of Bayesian nonlinear expectation in discrete time and its applications to capture drift and volatility uncertainties in modelling nonlinear time series. Applications for forecasting and risk measurement of Bitcoin as well as pricing Ethereum options are also considered.

This talk is mainly based on the following two papers.

1. Siu, T.K. Bayesian nonlinear expectation for time series modelling and its application to Bitcoin. Empirical Economics 64, 505–537 (2023). https://doi.org/10.1007/s00181-022-02255-z

2. Siu TK. Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty. Journal of Risk and Financial Management. 2024; 17(10):436. https://doi.org/10.3390/jrfm17100436

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