I will be investigating prophet inequalities, which are a subset of the theory of optimal stopping where the distribution of the random variables is known, and the development of the bounds associated with the inequalities over time. In this, I will aim to derive the bounds and note how improvements were made, and then run simulations in R to verify the bounds under specific scenarios regarding the distributions used (eg. independent and identically distributed). At the end, I wish to comment on the usefulness of the bounds and their implications on the real world
Joel Denning is a second-year student at Macquarie University undertaking a Bachelor of Actuarial Studies and a Bachelor of Science majoring in Mathematics. His research interests lie in the fields of probability and mathematics and how we can use statistics and probability to model real-world processes. Since completing his HSC in 2020, he has embraced the opportunity to guide others in their own HSC journeys, particularly those individuals’ studying mathematics and physics. In his free time, Joel loves to practice drums and catch up with his friends.