In this thesis, I derive the stochastic control formulation of the pricing model for popular riders in variable annuities with withdrawal guarantees, perform detailed mathematical analysis of the solution to the pricing model, and design efficient regression-based Monte Carlo simulation algorithms for solving the pricing model. In my first project, I present the detailed characterization of the pricing properties of the Guaranteed Minimum Withdrawal Benefits (GMWB) in variable annuities. Under certain limiting scenarios such as the large policy fund value, the time close to expiry, perpetuality of policy life or small value of guarantee account, we manage to obtain analytical approximate solution to the singular stochastic control model of dynamic withdrawals.

In my second pro...[ Read more ]

In this thesis, I derive the stochastic control formulation of the pricing model for popular riders in variable annuities with withdrawal guarantees, perform detailed mathematical analysis of the solution to the pricing model, and design efficient regression-based Monte Carlo simulation algorithms for solving the pricing model. In my first project, I present the detailed characterization of the pricing properties of the Guaranteed Minimum Withdrawal Benefits (GMWB) in variable annuities. Under certain limiting scenarios such as the large policy fund value, the time close to expiry, perpetuality of policy life or small value of guarantee account, we manage to obtain analytical approximate solution to the singular stochastic control model of dynamic withdrawals.

In my second project, I design the regression-based Monte Carlo simulation algorithms for solving the stochastic control models associated with pricing of the Guaranteed Lifelong Withdrawal Benefit (GLWB) in variable annuities, where the underlying fund value is assumed to follow the stochastic volatility models. Efficiency of the simulation procedure is enhanced by three techniques: dimension reduction via homogeneity property of the price value function; reduction of the strategy space through the bang-bang analysis; the derivation of the closed form solution for the price value function of the GLWB when the fund value becomes zero. We also conduct the sensitivity analysis of the GLWB price function subject to different model parameters, contractual features and assumptions on the withdrawal behavior of the policyholder.