Stochastic economic modeling for the deferred annuity (accumulation) line of business: Efficient modeling approaches for large and consolidated business blocks

Date of Completion

January 1999


Mathematics|Economics, Finance




This thesis develops a stochastic asset/liability model for the deferred annuity line of business. The model, Accumulation Stochastic Economic Model (ASEM), is a multifactor stochastic model that incorporates the important features of accumulation products and reflects stochastic economic scenarios to help management analyze and evaluate the profitability of the accumulation business line on a timely basis. We model an accumulation joint account that consists of the general account and separate account. The backing assets for the general account consist of 26 non-callable and 10 callable fixed income securities. We apply investment assumptions to these assets and develop a formula to calculate the model portfolio rate. Considering that the main use of the ASEM model is in Economic Value analysis and profitability evaluation, we allow the backing assets of the separate account to earn a fixed equity rate of return in order to keep our model simple. ^ To make our model flexible to assumption changes, we allow the input of asset parameters, new money rate, equity rate of return, deposit and withdrawal activities, surrender charge, surrender rate, minimum guarantees, and a dynamic fund transfer function. We anticipate that this model will be useful not only in profitability evaluation but also in risk analysis and cash flow testing for the accumulation business. This thesis also develops three efficient sampling algorithms for use in stochastic economic modeling for large/consolidated blocks of business. These algorithms are not limited to use in the accumulation business and can be extended to other insurance businesses as well. We have tested these algorithms with the ASEM model as well as commercial asset liability models and they prove to be effective in terms of running a small number of scenarios to obtain comparable results to a full model involving a large number of scenarios. With these algorithms and our proposed efficient modeling approaches, we make stochastic runs no longer time prohibitive for large/consolidated business blocks. Applications of the ASEM model and the sampling algorithms are introduced in this thesis. ^