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In many ways, public debt and pension fund managers share the same allocation problem: How to allocate optimally their assets and liabilities, assuming long-term uncertainties, complex business rules, and risk aversion. In that context, this thesis presents four studies, three from the point of view of public debt managers, and one from the point of view of closed defined benefits (DB) pension fund sponsors. We test the sensitivity of the optimal allocation to unexpected changes in life expectancy, to alternative macroeconomic environments, and to different aspects of pension funds regulation. The first study presents a new stochastic optimization model, based on the minimization of the certainty equivalent real carry cost of public debt, to compute optimal allocations for sovereign debt portfolios. We conduct five sensitivity exercises to test the consequences of different public policies and macroeconomic environments over the optimal liability allocation. The second study presents a stochastic simulation model to evaluate the main costs and risks associated with the issuance of longevity-linked bonds (LB) by governments. We conduct five exercises, in which we test the effects of the transition strategy, the relevance of choosing a correct design for LB, the longevity-risk premium, and two types of demographic shocks to simulate longevity risk. The third study presents a stochastic optimization model to assess the role of longevity-linked bonds in optimal sovereign debt portfolios. This model extends the first study, by incorporating demographic effects in fiscal policy, as well as the issuance of LB by governments. We conduct three exercises in which we test how the optimal allocation reacts to two types of demographic shocks and to alternative levels of the longevity-risk premium. The last study proposes a strategic asset allocation model for closed and mature DB schemes. The optimization criterion is to minimize a certainty equivalent cost for the pension scheme's sponsor that is defmed as the expected present value of the additional financial contributions (AFC) plus a fraction of their variance, the fraction characterizing the sponsor's risk attitude. AFC are determined by a rule that depends on the current funding ratio (FR), and two thresholds (minimum and maximum FR). We analyze four factors that influence the optimal asset mix: (i) the uncertainty about the remaining life expectancy of the beneficiaries, (ii) the expected equity return above a real (inflation adjusted) risk free rate, (iii) the time to restore the FR to normal levels, and (iv) the extent to which the sponsor can benefit from an asset surplus.

Achieving an adequate income in the old age to maintain the standard level of living after retirement has been a challenge to pension schemes for a long time. In fact, approaching this goal has led to a global pension crisis considering all the economic and demographic changes and the conflicting interests of employers and employees over time. This research aims to deriving different deterministic and stochastic dynamic pension funding models for defined benefit schemes within the mathematical framework of optimal control theory and dynamic programming. The practical implementation of these dynamic models into one of the largest Egyptian defined, benefit occupational pension schemes - as a case study - is a tool to examine how they act in the reality, and provide the management of the pension fund with a dynamic plan instead of the static ones that have been used in such a volatile market. Taking into consideration the optimal contribution rate of the mutual interests of both the employer and the employees by including a mixed middle term in the dynamic pension funding models. This represents both the contribution rate risk and the solvency risk and could provide a solution for one of the pension schemes problems.