Date of Completion

5-11-2013

Embargo Period

5-11-2013

Keywords

Efficient Modeling Techniques, Ratio Estimation, Replicated Sampling

Major Advisor

Prof. Jeyaraj Vadiveloo

Associate Advisor

Prof. Vladimir Podznyakov

Associate Advisor

Prof. Brian Hartman

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

Reliance on results from actuarial models for regulatory reporting as well as management decisions is increasing with complexity of financial products, economic volatility and the advancement of computing power. Sensitivity analysis is an important tool in modeling and is used to understand the impact of inputs and assumptions on the final result. However, we are constrained by computing time and resources, so the number of sensitivities that can be performed is limited.

Replicated Stratified Sampling (RSS) is a statistical technique that can be applied to efficiently run sensitivity tests on any actuarial model. We assume that model results with baseline assumptions are available for the full in-force block, and consider this as an auxiliary variable. The sensitivity of a model output to input variables is estimated using the ratio of the value of the model result with shocked assumptions to its value with baseline assumptions. The RSS estimator is developed as the average of ratio estimators with replicated stratified samples drawn from the in-force block. We consider a simple risk metric defined as the aggregate of a risk measure associated with each policy and show that the RSS ratio converges to the population ratio when the number of replications is increased, provided that the sample size is sufficiently large. We confirm this result through simulations and compare the RSS estimator with the traditional ratio estimator and Grouping, which is another technique that is commonly used in modeling.

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