Markowitz formalized portfolio selection as optimization of a quadratic program. Empirically, an optimal long portfolio is often sparse, which is somewhat at odds with general principle that the optimum should give weights to all things proportional to size. The framework of reproducing kernel Hilbert spaces, in particular kernel embeddings, allows one to rephrase the problem in a revealing way-- as in many diffusion type processes and complex variables, maximum principles give that optima must occur in some kind of distinguished boundary. Many physical maze solvers rely on the immensity of Avogadro's number, but approaches analogous to portfolio selection generically give finitary solutions.
Additional topics may include approaches to dynamics via Koopman operators, methods for creating new kernels with richer function theoretic structure from more basic ones, and unexploited aspects of reproducing kernels such as multipliers.
Copyright. All Rights Reserved.