This paper studies an optimal portfolio problem for a DC pension plan considering both interest rate risk and longevity risk . In the accumulation phase, plan members pay constant contributions continuously into the pension fund. We assume that the evolution of mortality rate of all the plan members can be described by the same stochastic process and a representative member is chosen to study the problem . At retirement time, the pension fund is used to purchase a lifetime annuity and a minimum guarantee is required by the representative member. To hedge the longevity risk , we introduce a mortality-linked security, i.e. a longevity bond , into the financial market . The pension manager makes investment decisions for the benefit and on behalf of the representative pension member whose objective is to maximize his expected utility of the terminal surplus between the final fund level and the minimum guarantee . To solve the initial constrained non-self-financing optimization problem , we transform it to an unconstrained self-financing problem by replicating the future contributions and the minimum guarantee . By applying dynamic programming method, analytical solutions to the equivalent optimization problem are derived and optimal investment strategies to the original problem are obtained by simple calculations. The numerical applications reveal that the longevity risk has an important impact on the investment strategies and show evidence that mortality-linked securities could provide an efficient way to hedge the longevity risk.
Pension schemes all over the world are under increasing pressure to efficiently hedge the longevity risk posed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pension scheme which decides to hedge the longevity risk using a mortality-linked security, typically a longevity bond . The pension scheme invests in the risky assets available in the market, including the longevity bond, by using the contributions from a representative scheme member to ensure a minimum guarantee such that the member is able to purchase a lifetime annuity upon retirement. We transform this constrained optimal investment problem into an unconstrained problem by replicating a self-financing portfolio of future contributions from the member and the minimum guarantee provided by the scheme. We solve the resulting optimisation problem using the dynamic programming principle and through a series of numerical studies reveal that the longevity risk has an important impact on the performance of investment strategies. Our results provide mathematical evidence supporting the use of mortality-linked securities for efficient hedging of the longevity risk.
R
This paper studies an optimal portfolio problem for a DC pension plan considering both interest rate risk and longevity risk . In the accumulation phase, plan members pay constant contributions continuously into the pension fund. We assume that the evolution of mortality rate of all the plan members can be described by the same stochastic process and a representative member is chosen to study the problem . At retirement time, the pension fund is used to purchase a lifetime annuity and a minimum guarantee is required by the representative member. To
Pension schemes all over the world are under increasing pressure to efficiently hedge the longevity risk posed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pension scheme which decides to
R
, we introduce
using
R
i.e.
typically
D
, into the financial market
R
manager makes investment decisions for the benefit and on behalf of the representative pension member whose objective is to maximize his expected utility of the terminal surplus between the final fund level and the minimum guarantee . To solve the initial constrained non-self-financing optimization problem , we transform it to an unconstrained self-financing
scheme invests in the risky assets available in the market, including the longevity bond, by using the contributions from a representative scheme member to ensure a minimum guarantee such that the member is able to purchase a lifetime annuity upon retirement. We transform this constrained optimal investment problem into an unconstrained
R
the future contributions
a self-financing portfolio of future contributions from the member
R
. By applying dynamic programming method, analytical solutions to the equivalent optimization problem are derived and optimal investment strategies to the original problem are obtained by simple calculations. The numerical applications
provided by the scheme. We solve the resulting optimisation problem using the dynamic programming principle and through a series of numerical studies
R
investment strategies and show evidence that
performance of investment strategies. Our results provide mathematical evidence supporting the use of
R
could provide an efficient way to hedge
for efficient hedging of