 Info
Asset/Liability Management in Life Insurance
Project Description
Asset/Liability
Management in Life Insurance
T. Gerstner
Much
effort has been spent on the development of stochastic
assetliability 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
longterm 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
marketbased, fair value accountancy standards as required by
Solvency II and the International Financial Reporting Standard.
Due to the wide range of pathdependencies, guarantees and optionlike
features of insurance products, closedform representations of
statistical target figures, like expected values or variances, which
in turn yield embedded values or riskreturn 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.
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 quasiMonte Carlo and
sparse grid methods in combination with adaptivity and dimension
reduction techniques for its numerical computation. QuasiMonte 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 have the potential to
significantly reduce the number of required scenarios and computing
times.
References

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

T. Gerstner, M. Griebel and M. Holtz:
Efficient deterministic
numerical simulation of stochastic assetliability management models
in life insurance.
Insurance:
Math. Economics,
44:434446,
2009.

T. Gerstner, M. Griebel and M. Holtz.
The effective dimension of
assetliability management problems in life insurance.
In Proc.
Third Brazilian Conference on Statistical Modelling in Insurance and
Finance,
pp. 148153, 2007.

T. Gerstner, M. Griebel, M. Holtz, R. Goschnick and M. Haep:
A
General AssetLiability Management Model for the Efficient
Simulation of Portfolios of Life Insurance Policies.
Insurance:
Math. Economics,
42(2):704716,
2008.

T. Gerstner, M. Griebel, M. Holtz, R. Goschnick and M. Haep:
Numerical
Simulation for AssetLiability Management in Life Insurance.
In
Mathematics
 Key Technology for the Future.
pp. 319341. Springer, 2008.