A Comparative Study of Risk Measures for Guaranteed Minimum Maturity Benefits by a PDE Method

Abstract

The stochastic modeling and determination of reserves and risk capitals for variable annuity guarantee products are relatively new developments in the insurance industry. The current market practice is largely based on Monte Carlo simulations, which have great engineering flexibility but the demand for heavy computational power can be prohibitive in many cases. In this paper, we distinguish and compare two types of risk models to determine the commonly used risk measures for reserving and capital calculations. Using an example of the guaranteed minimum maturity benefit, we investigate alternative numerical methods that require less computational resources and yet achieves high accuracy and efficiency.

Keywords: Variable annuity guaranteed benefit, actuarial risk management, numerical PDE method, quantile risk measure, conditional tail expectation.

JEL Classification: C63; G22; G17