Enhanced indexation is a portfolio optimization problem that aims to construct a portfolio capable of outperforming a benchmark while controlling downside risk and its relationship with the benchmark return distribution. Existing approaches based on second-order stochastic dominance often rely on a minimax criterion, focusing exclusively on the worst deviation from the benchmark across different conditional value-at-risk levels. This may lead to overly conservative portfolio choices.

Learn about a more flexible framework based on the Ordered Weighted Average operator. By assigning different weights to the ordered deviations from the benchmark, the model can move smoothly from worst-case optimization to a broader control of the return distribution. The approach also controls cumulative violations of stochastic dominance rather than considering only the single worst violation. 

Despite this additional flexibility, the resulting portfolio selection models can be formulated as linear programs and implemented efficiently in MATLAB^®. An out-of-sample analysis on major equity data sets shows how different OWA specifications can be used to emphasize either profitability and risk-adjusted performance or risk mitigation and portfolio stability. The framework therefore provides a transparent and tractable way to design enhanced indexation strategies for different investor preferences.

Goal-based wealth management provides a practical framework for aligning investment decisions with an investor’s specific financial objectives, such as retirement, education funding, home ownership, or wealth transfer—unlike approaches that focus primarily on outperforming a market benchmark. By organizing wealth around clearly defined goals, investors can adopt risk levels and investment strategies that are appropriate for each objective and its time horizon. As personal circumstances and financial priorities evolve, goal-based wealth management allows portfolios to be adjusted dynamically, ensuring that investment strategies remain aligned with the investor’s long-term aspirations and financial well-being.

Discover how to implement a reinforcement learning workflow on goal-based wealth management by offline reinforcement learning in MATLAB^®. Market sentiment data is incorporated as part of the environment state to capture changing market conditions and risk regimes. This market regime-aware extension allows the policy to adapt dynamically under different market conditions while remaining within the same reinforcement learning framework.

Financial application is for illustrative purposes only.

This research develops a two-dimensional finite element method (FEM) solver for pricing European call options under the Heston stochastic volatility model, formulated in log-moneyness–variance coordinates (y, v) with linear P1 elements and a Rannacher-stabilized θ-scheme in time. The resulting baseline surface is validated through mesh refinement studies (N = M ∈ [40, 100]), showing stable pointwise and mid-region L2 errors, and through structural sanity checks confirming positivity, near-monotonicity in spot, and adherence to no-arbitrage bounds 0 ≤ CFEM ≤ S. Robustness is assessed by comparing the Heston FEM against a one-dimensional Black–Scholes FEM solver on the same grid, and against semi-closed-form analytic Heston prices. On a restricted mid-range region, the FEM solution exhibits a systematic but small underpricing bias (97.7% of grid points), with mean relative error of 2.27%. These results support the structural correctness of the solver while identifying limitations tied to linear  elements and mild stabilization, motivating future work on adaptive meshing, higher-order discretizations, and market calibration.