New Safe Approximation of Ambiguous Probabilistic Constraints for Financial Optimization Problem

Abstract

In financial optimization problem, the optimal portfolios usually depend heavily on the distributions of uncertain return rates. When the distributional information about uncertain return rates is partially available, it is important for investors to find a robust solution for immunization against the distribution uncertainty. The main contribution of this paper is to develop an ambiguous value-at-risk (VaR) optimization framework for portfolio selection problems, where the distributions of uncertain return rates are partially available. For tractability consideration, we deal with new safe approximations of ambiguous probabilistic constraints under two types of random perturbation sets and obtain two equivalent tractable formulations of the ambiguous probabilistic constraints. Finally, to demonstrate the potential for solving portfolio optimization problems, we provide a practical example about the Chinese stock market. The advantage of the proposed robust optimization method is also illustrated by comparing it with the existing optimization approach via numerical experiments.

A New Data-Driven Distributionally Robust Portfolio Optimization Method Based on Wasserstein Ambiguity Set

“…For more recent researches on portfolio optimization, the reader may refer to [3]- [5], which provides a useful reference for handling portfolio selection problems for both researchers and practitioners. The core of modern portfolio theory involves balancing return and risk, determining an effective portfolio strategy, and allocating capital to multiple available assets, to minimize risk while maximizing returns [6]. In the case of maximizing the portfolio return while minimizing risk, the optimal portfolio strategy depends heavily on the underlying hypothesis on the uncertainty of asset return and the choice of risk measure.…”