This project aims to develop efficient AI solution methodologies for solving long-standing financial optimization problems and challenging issues that are emerging. The final deliverable will be a software system which includes a family of solution packages for different financial decision problems.
The past half-century has witnessed a remarkable advancement in modern financial decision theory and practice, both in enhancing our fundamental understanding of market randomness, and in enabling market participants to harness appropriate risk for a better return.
Still, many financial decision-making and risk management problems remain open and challenging, and are nonconvex in nature. Essentially, if we incorporate real world considerations into our financial decision-making models (for example, investors’ asymmetric risk attitude towards gain and loss), we will be surrounded by a nonconvex world. One example is the mean-Value-at-Risk (VaR) portfolio selection problem, which is both nonconvex and discontinuous. In fact, the real financial world generates endless lists of nonconvex optimization problems, including portfolio selection under high-moment risk measures (skewness and kurtosis for example), cardinality constrained portfolio selection, risk parity strategy, tax-loss harvesting, and fixed income portfolio.
A long list of efforts from optimization, statistics and machine learning has led to relatively efficient algorithms for solving nonconvex optimization problems: stochastic gradient descent, momentum regularization, variance reduction, and mini-batch optimization. Also neurodynamics-based portfolio optimization deserves in-depth investigation in its own right because of the distinctive complexities in depth and scale of financial engineering and management.