Why Actuarial Reserve Projections Are Calculated Backward

Summary

This note explains why an actuarial projection of annuity reserves may proceed backward from the end of the projection horizon. At each time, the reserve represents the present value of expected future payments from that point onward. Starting at the final time, when the reserve is assumed to be zero after all payments have ended, allows earlier reserves to be calculated recursively from the next period’s reserve, cashflows, and discounting.

The questioner suggests that this reverse calculation avoids first valuing all payments and then repeatedly aggregating future cashflows for each projection time. The document frames this as a computational convenience in reserve calculations rather than a claim that the underlying cashflows themselves occur backward. It offers a conceptual explanation but no formulas, numerical example, or comparison of computational costs. The approach also depends on the terminal assumption: if liabilities remain at the chosen horizon, the terminal reserve cannot simply be set to zero.

Key ideas

• An actuarial reserve at a projection time is the present value of expected future cashflows from that time onward.
• Backward recursion starts from a terminal reserve and calculates earlier reserves in sequence.
• The terminal reserve is set to zero in the example because the projection ends after payments have ceased.
• Reverse calculation can avoid repeatedly aggregating all later cashflows at every time point.
• The terminal assumption must reflect whether any liabilities remain at the projection horizon.

Tags

# Why are cashflows "modelled backwards in time"?


# Why are cashflows "modelled backwards in time"?












A am currently reading a manual on how to use some actuarial modelling software to project the expected liability payments made under an annuity contract. In this guide, the following statement is made:

> In financial modelling we start at the point when everyone has died. This is the oldest age in our mortality table.

Could anyone explain to me why it would be preferable to model these cashflows backwards in time, rather than forwards?

Addendum: Having written out this question, I think I might have realised the answer for my self (but please do correct/verify my assertion).

The purpose of actuarial models is often to calculate the reserve that should be held at each projection time. Thus, at a given projection time, say $t$, we need to know the present value of all future expected cashflows (i.e. the present value of all cashflows at times $>=t$). This would give rise to a greater computational overhead if we first calculated the EPV of all payments, and then aggregated to calculate the reserve

Thus, we instead work backwards to from the maximum projection term, when the reserve held is assumed to be zero, back to time 0.

I suppose that the manual should instead have said: "When modelling reserves we start at the point when everyone has died".

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.