Quantum-inspired Risk Portfolio Optimization via Exponential Tilting

Financial portfolio optimization is often framed through mean-variance objectives, yet real profit-and-loss (P&L) scenario distributions are typically discrete and non-Gaussian. To explore realistic P&L distributions, we propose an objective function based on exponential tilting and certainty equivalent under constant absolute risk aversion. We then derive a second-order approximation, recovering a quadratic optimization problem solvable through mixed integer quadratic programming (MIQP) and quadratic unconstrained binary optimization (QUBO). Constraints in the QUBO formulation are incorporated via Lagrangian relaxation and slack variable approaches, enabling a direct comparison between classical constrained MIQP and quantum-inspired methods. In order to study how exponential tilting affects mean, standard deviation, and tail-risk measures such as Value at Risk and Conditional Value at Risk, we design an experimental protocol based on scanning a grid of tilt parameters and solving the associated optimization problems. The results on a realistic trading portfolio show how the tilts can be tuned to optimize different risk-return profiles while remaining competitive with those found using other state-of-the-art approaches. Moreover, performance analysis suggests that, even using classical solvers, the QUBO formulation with Lagrangian relaxation scales better than the MIQP approach, providing the best constraint encoding strategy.