Date of Completion


Embargo Period



Stochastic financial planning, Markov Chain Monte Carlo (MCMC) simulations, formulating method, quantile optimization, non-linear optimization model, Lagrange method

Major Advisor

Jeyaraj Vadiveloo

Associate Advisor

Emiliano Valdez

Associate Advisor

Guojun Gan

Field of Study



Doctor of Philosophy

Open Access

Open Access


The traditional algorithmic approach of financial planning is based on Monte Carlo simulations of yield curves and mortality. Financial advisors determine the withdrawal amount under an acceptable level of failure (target ruin) in the simulated future cash flows by using trial and error methods. The number of iterations with full credibility has allowed financial advisers and software systems to be precise about calculating a withdrawal level that achieves a target ruin. However, it is always extremely time-consuming (several hours or days).

Rather than try and determine the optimal withdrawal level, this research creates a formulaic method to obtain a closed-form solution of the maximum withdrawal for each simulated scenario. And then we choose the quantile (target ruin) of all the maximum withdrawals as the final optimal solution. The runtime is dramatically decreased (within seconds). Based on this methodology, this research has also built a non-linear optimization model using an adjusted Lagrange method to solve the optimal allocation of each asset in the portfolio which can result in the optimal withdrawal level.