The FA-SAA Algorithm for CVaR Optimization

This paper develops a unified algorithm to address the Conditional Value at Risk (CVaR) optimization problem characterized by two levels of expectations, where the inner-level expectation handles the repricing of the financial instruments and the outer-level expectation represents the risk measure. We propose an FA-SAA algorithm that tackles the inner-level expectation through function approximation (FA) method and addresses the outer-level expectation by sample average approximation (SAA). A variety of machine learning methods can be incorporated into this algorithm and eventually the optimization problem is reformulated into a linear programming problem, whose optimal value and optimal solution converge to the actual ones. Besides, we demonstrate that the convergence rate of optimal value can achieve OP(Γ-1/2). The numerical results substantiate the efficacy of our proposed algorithm.