Beyond Physical Maze Solvers via Modern Portfolio Theory

Explore the intersection of portfolio theory and maze-solving algorithms in this 47-minute conference talk by James Pascoe from Drexel University. Delve into how Markowitz's portfolio selection optimization can be applied beyond finance to solve complex problems. Examine the empirical observation of sparse optimal long portfolios and its implications. Discover how reproducing kernel Hilbert spaces and kernel embeddings offer a new perspective on optimization problems, drawing parallels to diffusion processes and complex variables. Investigate the role of maximum principles in determining optima on distinguished boundaries. Compare physical maze solvers relying on Avogadro's number with finitary solutions derived from portfolio selection approaches. Gain insights into additional topics such as Koopman operators for dynamics analysis, methods for creating advanced kernels, and unexplored aspects of reproducing kernels like multipliers. Recorded at IPAM's Analyzing High-dimensional Traces of Intelligent Behavior Workshop, this talk offers a unique perspective on problem-solving techniques that bridge financial theory and computational algorithms.