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Stochastic approach to pension funding, allowing for the pension accrual density function

Economou, M. (2003). Stochastic approach to pension funding, allowing for the pension accrual density function. (Unpublished Doctoral thesis, City, University of London)


The thesis introduces a different insight into the traditional methods of pension funds by implementing two ideas:

(a) To consider the age of the plan participant in the development of the pension scheme as an additional factor that affects the growth of the Fund and the determination of the Contribution rates. This is attempted by the pension purchase density function ‘m(x)’ which is viewed as a probability density function. ‘ New Cost methods ‘ are defined based on the statistical distributions: Power function, Truncated Pareto and Truncated Exponential.

(b) To consider the parameter A’, that determines how quickly the Unfunded Liabilities are covered, as a random variable; A’ takes values around a fixed value zone, which is considered as the expected value of the random variable.

We build a theoretical model, independent of the distributional assumptions, that has run on the fundamental bases, where either each of the rates of investment return and A’ or both are random variables. The first and second moments of the Fund and Contribution rates are calculated, as well as their ultimate values as time ‘t’ tends to infinity.

A simulation analysis is performed assuming that either or both parameters (i(t)A(t)) are random with a Log Normal distribution. In addition, for either case, we assumed that the pension plan is implemented based on a different pension accrual density function each time. On the basis of the simulated data, the 3rd , 4th moments and the percentile values of the Fund and Contribution levels are calculated.

Conclusions derived for both the Actuarial liability level under the ‘New Cost Methods’ and the growth of the Fund on each basis of the theoretical model. In particular we show that a) the development of Normal Cost follows the pattern of the accrual function ‘m(x)’ and b) the Actuarial Liability is higher under the density function that allocates larger proportions of the benefit at younger ages. We also specify an ‘optimal region’, m , for the number of years, m, over which the unfunded liability is spread. We show that for m greater than a particular value m the variances of both the fund and the contribution are increasing functions of m. The conclusions are confirmed by the simulation data.

The results raise questions such as the important issue of dependency between the rates of investment return and the spread parameter. These questions imply the extension of this work allowing for further steps in the future.

Publication Type: Thesis (Doctoral)
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Departments: Bayes Business School > Actuarial Science & Insurance
Bayes Business School > Bayes Business School Doctoral Theses
Doctoral Theses
[thumbnail of Economou thesis 2004 PDF-A.pdf]
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