It is common practice for public pension schemes to offer individuals the option to delay benefit claiming until after the normal retirement age, and increase the annual benefit level as a result. Existing literature shows that for non-liquidity constrained individuals, delaying benefit claiming for a number of years after retirement is optimal from a utility perspective in a wide variety of cases. In this paper we focus on non-liquidity constrained individuals who wish to defer pension benefits, and investigate the attractiveness of an alternative deferral strategy. The alternative deferral strategy consists of claiming benefits immediately, and using them to buy deferred annuities from an insurance company. We first determine conditions under which the accrual offered by the public pension scheme for delaying benefit claiming is less than actuarially fair from the viewpoint of an insurer who uses the prevailing term structure of interest rates to determine the expected present value of missed and additional benefits. Actuarial unfairness can be generated by, e.g., age-independent accrual rates or slow adjustments of the accrual rates to changes in interest rates. We find that, in particular for men, the degree of actuarial unfairness is such that there is ample room for insurers to profitably offer annuity products that make the alternative deferral strategy preferred to deferring benefit claiming. If individuals choose to strategically exploit these alternative deferral strategies, this will affect benefit claiming behavior in public pension schemes, which in turn affects long run program costs.