Optimization and Simulation of a Defined Contribution Pension System for Faculty Under Certainty and Uncertainty

In recent years, the increasing complexity and risk exposure of pension systems have ledresearchers to adopt hybrid approaches that integrate simulation and optimization techniques to support strategic decisions. Simulation methods, particularly Monte Carlo and scenariobased simulations, have been widely applied to capture uncertainties related to asset returns, salary progression, interest rates, and mortality risk (Boulier et al., 1995; Haberman and Vigna, 2002). These simulations enable the modeling of dynamic systems over long horizons and provide insight into the stochastic nature of pension outcomes. Parallel to this, optimization techniques—especially stochastic control, dynamic programming, and quadratic programming—have been employed to derive optimal asset allocations and contribution strategies. For example, Cairns et al. (2006) introduce a stochastic lifestyling model for defined contribution plans, optimizing investment strategies based on salary risk and annuity constraints. Similarly, Consiglio et al. (2015) develop a stochastic programming model to design and price guarantee options in DC plans, balancing cost and embedded risks. Shen and Sherris (2017) extend these methods by integrating stochastic mortality, income, and interest rate models into a unified lifetime optimization framework. Their work illustrates how both idiosyncratic and systematic longevity risks influence investment, consumption, and insurance strategies over an individual’s ifetime. Together, these studies show that combining simulation with optimization provides a robust toolkit for assessing pension policy reforms, designing dynamic investment strategies, and evaluating guarantee mechanisms under demographic and financial uncertainty. This integrated approach enhances the capacity to make informed, resilient decisions that align long-term financial sustainability with retirees’ welfare. This work synthesizes a series of studies addressing pension planning for academic personnel at Mexican higher education institutions. The first study, presented at the 2020 ICPR-Americas conference, introduced a linear optimization model developed in LINGO to determine the minimum salary contribution rate required to ensure retirement coverage over a desired number of years. The model incorporates key economic variables such as inflation, salary increases, and interest rates. Results showed that a contribution rate of approximately 13% was necessary to provide sufficient retirement income over a 10- to 20-year post-retirement period. Building upon this foundation, the 2025 article in Computation presents a deterministic multi-objective optimization model designed to both minimize the ontribution rate and maximize post-retirement coverage. Implemented in LINGO, the model evaluates three realistic economic scenarios under varying inflation rates and retirement needs. It produces Pareto-optimal solutions, revealing that optimal contribution rates can range from 10% to 80% of salary depending on assumptions, particularly inflation and desired income replacement levels. The study published in 2024 in Computational Statistics, applies a stochastic simulation model using Arena software to analyze a defined contribution retirement scheme. The simulation incorporates faculty age, seniority, salary dynamics, and attrition probabilities. The results show that an increase in the number of simulation replicas significantly impacts the precision and stability of average capital estimates. When moving from 30 to 300 replicas, the mean capital increases from 479.79 to 509.46 thousand MXN, and the 90% confidence interval for this mean becomes noticeably narrower, shrinking from a range of [435.56, 524.03] to [495.21, 523.71] thousand MXN. This reduction in interval width is clear evidence of increased reliability in the average capital estimation. When simulating with 1000 replicas, the mean capital further stabilizes at 510.45 thousand MXN, and the 90% confidence interval contracts to an even more precise range of [502.75, 518.15] thousand MXN. This reaffirms that a higher number of simulations leads to a more robust estimate with less uncertainty. A consistent finding across all scenarios is the 5% Value at Risk (VAR 5%), which remains at 27.82 thousand MXN. This indicates that 5% of capital outcomes fall below this value, suggesting stability in the lower capital thresholds, regardless of the number of replicas used. Finally, the Coefficient of Variation (CV), although showing a slight decrease with more replicas (from 108.56% to 102.50%), consistently remains above 100%. This high CV underscores a considerable relative variability in the capital data. This elevated dispersion implies that, while the mean becomes more precise with more replicas, the intrinsic variability of teachers’ capital is a prominent characteristic that must be considered in risk assessment. In summary, the simulation results improve in precision and stability as the number of replicas increases, which is fundamental for informed decision-making within a pension system.. Together, these studies demonstrate the value of combining optimization and simulation techniques to inform institutional pension planning, offering robust tools for decision-makers navigating the evolving landscape of retirement systems in Mexico.