THESIS
2014
xiv, 124 pages : illustrations ; 30 cm
Abstract
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...[
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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.
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