Asset Liability Management

© Photo Fraunhofer SCAI

Much effort has been spent on the development of stochastic asset-liability management (ALM) models for life insurance companies in the last years. Such models are becoming more and more important due to new accountancy standards, greater globalisation, stronger competition, more volatile capital markets and long periods of low interest rates. They are employed to simulate the medium and long-term development of all assets and liabilities. This way, the exposure of the insurance company to financial, mortality and surrender risks can be analysed. The results are used to support management decisions regarding, e.g., the asset allocation, the bonus declaration or the development of more profitable and competitive insurance products. The models are also applied to obtain market-based, fair value accountancy standards as required by Solvency II and the International Financial Reporting Standard.

Due to the wide range of path-dependencies, guarantees and option-like features of insurance products, closed-form representations of statistical target figures, like expected values or variances, which in turn yield embedded values or risk-return profiles of the company, are in general not available. Therefore, insurance companies have to resort to numerical methods for the simulation of ALM models. In practice, usually Monte Carlo methods are used which are based on the averaging of a large number of simulated scenarios. These methods are robust and easy to implement but suffer from an erratic convergence and relatively low convergence rates. In order to improve an initial approximation by one more digit precision, Monte Carlo methods require, on average, the simulation of a hundred times as many scenarios as have been used for the initial approximation. Since the simulation of each scenario requires to run over all relevant points in time and all policies in the portfolio of the company, often very long computing times are needed to obtain approximations of satisfactory accuracy. As a consequence, a frequent and comprehensive risk management, extensive sensitivity investigations or the optimisation of product parameters and management rules are often not possible.

© Photo Fraunhofer SCAI

In this project, we focus on approaches to speed up the simulation of ALM models. To this end, we rewrite the ALM simulation problem as a multivariate integration problem and apply quasi-Monte Carlo and sparse grid methods in combination with adaptivity and dimension reduction techniques for its numerical computation. Quasi-Monte Carlo and sparse grid methods are alternatives to Monte Carlo simulation, which are also based on a (weighted) average of different scenarios, but which use deterministic sample points instead of random ones. They can attain faster rates of convergence than Monte Carlo, can exploit the smoothness of the integrand and have deterministic upper bounds on their error. In this way, they can significantly reduce the number of required scenarios and computing times.


  1. T. Gerstner and M. Griebel:
    Sparse grids.
    In Encyclopedia of Quantitative Finance, J. Wiley & Sons, 2009.

  2. T. Gerstner, M. Griebel and M. Holtz:
    Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance.
    Insurance: Math. Economics, 44:434-446, 2009.

  3. T. Gerstner, M. Griebel and M. Holtz.
    The effective dimension of asset-liability management problems in life insurance.
    In Proc. Third Brazilian Conference on Statistical Modelling in Insurance and Finance, pp. 148-153, 2007.

  4. T. Gerstner, M. Griebel, M. Holtz, R. Goschnick and M. Haep:
    A General Asset-Liability Management Model for the Efficient Simulation of Portfolios of Life Insurance Policies.
    Insurance: Math. Economics, 42(2):704-716, 2008.

  5. T. Gerstner, M. Griebel, M. Holtz, R. Goschnick and M. Haep:
    Numerical Simulation for Asset-Liability Management in Life Insurance.
    In Mathematics - Key Technology for the Future. pp. 319-341. Springer, 2008.