Optimal Stopping Differential Equations

Optimal stopping describes a scenario where we are constantly receiving new information while the future is still uncertain, and we are challenged with finding the optimal time to undertake a specific action to achieve the most ideal outcome. These methods are used to evaluate real options, as they can model and predict the value of a firm whilst accounting for uncertainty of future information and unforeseen impacts on the market.

This research aims to develop extensions to an existing differential equation used to determine optimal stopping times, to model more sophisticated contexts. The model will be extended by applying game theoretic principles to analyse the behaviour of multiple actors participating in the market. This will ultimately assist investors when making decisions in the context of real options.

Patrick Daley

Macquarie University

Patrick Daley is a Dean’s Scholar at Macquarie University, studying a Bachelor of Actuarial Studies and a Bachelor of Mathematical Sciences, majoring in applied mathematics. He is excited to embark on his first-ever research project through the AMSI VRS over the summer on optimal stopping times. Patrick’s project draws on his background studying applied mathematics and probability to explore connections between optimal stopping, game theory, and ordinary differential equations.

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