Stochastic Optimization Based Decision Support System for Asset-liability Management in Life Insurance Firms

Abstract

Asset Liability Management (ALM) is a critical part of financial planning for all financial institutions. ALM deals with the management of a mismatch between the assets and liabilities of such firms both in value as well as in duration or maturity. Future uncertainty related to asset returns and liability outflows makes dealing with this problem a complex and challenging modeling problem. There are several published literature on application of Decision Support System (DSS) in process manufacturing industries but published literature is very scarce in the development of a DSS for addressing the ALM problem. A financial institution like a life insurance firm faces uncertainty on both its assets side as well as its liability side. While several work has been done in addressing the uncertainty through stochastic optimization model (Dantzig, 1955; Domenica, Mitra, Valente, & Birbilis, 2007; Sen & Higle, 1999) with recourse such models are generally difficult to comprehend by managers. Hence these models, although useful to managers for managing uncertainty are generally ignored. In this dissertation we introduce a Multi-stage Stochastic Optimization based Decision Support System (DSS) for Strategic planning in a life insurance firm.

This DSS is based on five fundamental elements: Assets, Liabilities, Accounts, Times and Scenarios. Through this DSS, we demonstrate that although stochastic optimization model is difficult to comprehend, we can develop a DSS where financial planning can be done with little or no knowledge of Optimization techniques. The implemented optimization model optimizes a linear function of expected value of the overall reserves (at the end of time horizon) while minimizing any shortfall encountered in between. The model employs a 768 scenario set over a 5 year horizon with a staggered scenario structure (12-8-4-2-1). The database implementation and linear program generation are executed on the 4D design environment. CPLEX is used in the optimization stage. We discuss several issues related to database development, user interface and financial planning. We also discuss several performance measurement of stochastic optimization models.

1. Various studies have been carried out to address the asset-liability management problem (M I Kusy & Ziemba, 1986; Vlerk, Klein Haneveld, & Drijver, 2000). Under deterministic asset parameters and liabilities, such a problem of resource allocation can be addressed by linear programming models. But under stochastic conditions, this problem becomes more complex. Stochastic optimization is one such tool that enables decision making under uncertain conditions. It furthers the advantages of linear programming by taking into account the randomness of various parameters (scenarios) for optimal resource allocation by scenario generation process. A comprehensive scenario set would enable the model to optimize its decisions more rigorously. As the number of scenarios taken into consideration increases, the scale of the problem increases. Even though real life problems can be tackled by large scale mathematical models, the acceptance of such models to a decision maker is contingent on their ease of use. 2. The performance of the firm is dependent on the firm’s abilities to generate investment returns over and above their liability commitments. The returns generated from its investments are uncertain owing to the economic conditions and performance of the underlying assets. The liability commitments are also influenced by the economic conditions. Additionally, these commitments are dependent on the life expectancy (mortality rates) of the insurees. Studies ((D. R. Carino et al., 1994; J. M. Mulvey, Ziemba, & Thorlacius, 1998)) on ALM in an insurance firm discuss models either based on deterministic liabilities or on liabilities dependent only on economic conditions. The studies incorporating impact of uncertain mortality rates in the insurance segment have focused primarily on assessing solvency risks of insurance firms but not on optimal resource allocation.

Through this DSS, we test the model using End-of-Period reserve worth as return measures and Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) at both 1% and 5% levels as risk measures. Value of Stochastic Solution (VSS) is also tracked to assess the improvement over mean value (MV) solution.

We were able to demonstrate a comprehensive DSS for asset-liability management for life insurance firms. We were also able to demonstrate the flexibility of this DSS by performing multiple experiments. We were also able to identify the value of using stochastic liabilities in the model.

From the experiments done using the DSS, the advantages of stochastic implementation are clearly observed as available in existing literature. In this dissertation, we were also able to identify the specific improvement in the solution with an increase in the number of scenarios under consideration. As the scenario set size increases, improvements are observed in both risk and return measures, thus indicating that more information is being captured in a larger scenario set. The improvement is large enough to advocate the implementation of a stochastic model with a large scenario set. Impact of introducing uncertainties in the liabilities is observed by running a model with only stochastic assets versus a model with stochastic assets as well as stochastic liabilities. It is clearly seen that incorporating uncertainties in the liabilities results in improvement in the risk and return measures as compared to a model with deterministic liabilities. Significant impact is also observed in the value of stochastic solution in the model with stochastic liabilities.