  The underlying stochastic nature of the requirements for the Solvency II
regulations has introduced significant challenges if the required calculations
are to be performed correctly, without resorting to excessive approximations,
within practical timescales. It is generally acknowledged by practising
actuaries within UK life offices that it is currently impossible to correctly
fulfil the requirements imposed by Solvency II using existing computational
techniques based on commercially available valuation packages. Our work has
already shown that it is possible to perform profitability calculations at a
far higher rate than is achievable using commercial packages. One of the key
factors in achieving these gains is to calculate reserves using recurrence
relations that scale linearly with the number of time steps. Here, we present a
general vector recurrence relation which can be used for a wide range of
non-unit linked policies that are covered by Solvency II; such contracts
include annuities, term assurances, and endowments. Our results suggest that by
using an optimised parallel implementation of this algorithm, on an affordable
hardware platform, it is possible to perform the `brute force' approach to
demonstrating solvency in a realistic timescale (of the order of a few hours).
