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Abstract

The main area of concern of this thesis is the development of the area of pension mathematics dealing with the funding of Defined Benefit pension schemes.

Particular attention is directed to the modelling of a stochastically evolving structure, whereby the demographic and financial variables may differ from the expectations, according to specific probability distributions.

In such a framework, we investigate how to efficiently combine exogenous variables, such as the level of contributions and the asset allocation, with the goal of devising an optimal risk management of pension funds.

The development of a stochastic model for the demographic evolution of the scheme is central for describing the dynamics of a pension scheme. Thus, the population plan theory, as presented in the literature, is extended, allowing for a random evolution of the membership population. Furthermore, the impact of this uncertainty is measured with and without the coexistence of a randomly evolving financial world.

For a pension scheme, the main sources of funding are the contribution paid by the sponsor and the returns from investing the available funds. The way of combining these two sources of income is a key issue in the determination of the risk profile and the costs of implementing a pension plan.

Using mathematical models and numerical algorithms, several contribution strategies are investigated, emphasising the aspects related to the risk and cost borne by the pension scheme. Specifically, the following intuitive insight, that a higher security is achieved by spending more, is found in analysing the profiles of different contribution strategies. Moreover, the impact on this trade-off between risk and cost is illustrated by separating the different effects of several sources of uncertainty. Finally, optimal contribution strategies are found analytically and numerically.

The allocation of the available funds is also taken into account, with the specific aim of identifying the optimal proportions of investment in a range of three possible assets. This issue, which is part of a broader discussion on the fundamentals of pension funding, is also considered together with the choice of the contribution strategy. The main result is that, when the two strategies are contextually developed, optimality is reached when there is support between the two strategies. In other words, within certain boundaries, it is optimal to combine a contribution strategy, which extensively relies on investment returns, with a high proportion of risky assets in the investment portfolio.

Avenues for further research are also suggested.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HG Finance Q Science > QA Mathematics
Departments:	Bayes Business School > Actuarial Science & Insurance > Statistical Research Reports Bayes Business School > Bayes Business School Doctoral Theses Doctoral Theses

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