Quantitative Methods Pension Fund Optimal Allocations

2004

In this paper we propose a continuous time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. Traditionally, portfolio selection models are interested in maximizing the total expected discounted utility from consumption and from final wealth, whereas our target is to maximize the total expected discounted utility from current wealth. In our model the dynamics of wealth takes directly into account the flows of contributions and benefits, so that in general the portfolio is not self-financing and the level of wealth is constrained to stay above a “solvability level”. The fund manager can invest in a riskless asset and in a risky asset but borrowing and short selling are prohibited. Pension funds are exposed to financial and demographic risks, but in our model we consider these risks stochastically independent and we only analyze the financial aspects. Although this is the common assumption, it is questionable and we leave the inclu...

Insurance: Mathematics and Economics, 2001

We consider a dynamic model of pension funding in a defined benefit plan of an employment system. The prior objective of the sponsor of the pension plan is the determination of the contribution rate amortizing the unfunded actuarial liability, in order to minimize the contribution rate risk and the solvency risk. To this end, the promoter invest in a portfolio with n risky assets and a risk-free security. The aim of this paper is to determine the optimal funding behavior in this dynamic, stochastic framework.

Managerial Finance, 2006

Purpose of this paper: we study the asset allocation problem for a pension fund which maximizes the expected present value of its wealth augmented by the prospective mathematical reserve at the death time of a representative member. Design/methodology/approach: we apply the stochastic optimization technique in continuous time. In order to present an explicit solution we consider the case of both deterministic interest rate and market price of risk. Findings: we demonstrate that the optimal portfolio is always less risky than the one. In particular, the asset allocation is less and less risky until the pension date while, after retirement of the fund's representative member, it becomes riskier and riskier.

Journal of Economic Dynamics & Control, 2006

This paper considers the asset-allocation strategies open to members of definedcontribution pension plans. We investigate a model that incorporates three sources of risk: asset risk and salary (or labour-income) risk in the accumulation phase; and interest-rate risk at the point of retirement. We propose a new form of terminal utility function, incorporating habit formation, that uses the plan member's final salary as a numeraire. The paper discusses various properties and characteristics of the optimal stochastic asset-allocation strategy (which we call stochastic lifestyling) both with and without the presence of non-hedgeable salary risk. We compare the performance of stochastic lifestlying with some popular strategies used by pension providers, including deterministic lifestyling (which involves a gradual switch from equities to bonds according to preset rules) and static strategies that invest in benchmark mixed funds. We find that the use of stochastic lifestyling significantly enhances the welfare of a wide range of potential plan members relative to these other strategies.

2010

In this paper we study the optimal management of an aggregated pension fund of defined benefit type, in the presence of a stochastic interest rate. We suppose that the sponsor can invest in a savings account, in a risky stock and in a bond with the aim of minimizing deviations of the unfunded actuarial liability from zero along a finite time horizon. We solve the problem by means of optimal stochastic control techniques and analyze the influence on the optimal solution of some of the parameters involved in the model.

European Financial Management, 2011

We model the asset allocation decision of a stylised corporate defined benefit pension plan in the presence of hedgeable and unhedgeable risks. We assume that plan fiduciaries -who make the asset allocation decision -face non-linear payoffs linked to the plan's funding status because of the presence of pension insurance and a sponsoring employer who may share any shortfall or pension surplus. We find that even simple asymmetries in payoffs have large and highly persistent effects on asset allocation, while unhedgeable risks exert only a small effect. We conclude that institutional details are crucial in understanding DB pension asset allocation.

This paper considers the asset allocation strategies for members of defined-contribution pension plans with exponential utility when there are three types of asset, cash, bonds and stocks. The portfolio problem is to maximize the expected utility of terminal wealth that uses the plan member's final wage as a numeraire, in the presence of three risk sources, interest risk, asset risk and wage risk. The use of a stochastic numeraire makes usual riskless cash assets risky. A closed form solution is found for the asset allocation problem when a portfolio replicates exactly the wage process exists, which is the true riskless asset. T he optimal portfolio composition is horizon dependent, while the investments in the three asset classes have constant wealth-to-wage ratios. The paper discusses the implication of using wage as numeraire and assuming exponential utility function in portfolio and pension investment strategy studies.

European Journal of Operational Research, 2008

In this paper we study the problem of simultaneous minimization of risks, and maximization of the terminal value of expected funds assets in a stochastic defined benefit aggregated pension plan. The risks considered are the solvency risk, measured as the variance of the terminal fund's level, and the contribution risk, in the form of a running cost associated to deviations from the evolution of the stochastic normal cost. The problem is formulated as a bi-objective stochastic problem of mean variance and it is solved with dynamic programming techniques. We find the efficient frontier and we show that the optimal portfolio depends linearly on the supplementary cost of the fund, plus an additional term due to the random evolution of benefits.

This paper proposes an Asset Liability Management (ALM) multistage stochastic programming model and a new method for measuring and controlling the equilibrium risk of a pension fund in the Brazilian context.

Journal of Risk and Financial Management, 2022

A retiree with a savings account balance, but without a pension, is confronted with an important investment decision that has to satisfy two conflicting objectives. Without a pension, the function of the savings is to provide post-employment income to the retiree. At the same time, most retirees want to leave an estate to their heirs. Guaranteed income can be acquired by investing in an annuity. However, that decision takes funds away from investment alternatives that might grow the estate. The decision is made even more complicated because one does not know how long one will live. A long life expectancy may require more annuities, and a short life expectancy could promote more risky investments. However there are very mixed opinions about both strategies. A framework has been developed to assess consequences and the trade-offs of alternative investment strategies. We propose a stochastic programming model to frame this complicated problem. The objective is to maximize expected esta...