  We propose a class of discrete-time stochastic models for the pricing of
inflation-linked assets. The paper begins with an axiomatic scheme for asset
pricing and interest rate theory in a discrete-time setting. The first axiom
introduces a "risk-free" asset, and the second axiom determines the
intertemporal pricing relations that hold for dividend-paying assets. The
nominal and real pricing kernels, in terms of which the price index can be
expressed, are then modelled by introducing a Sidrauski-type utility function
depending on (a) the aggregate rate of consumption, and (b) the aggregate rate
of real liquidity benefit conferred by the money supply. Consumption and money
supply policies are chosen such that the expected joint utility obtained over a
specified time horizon is maximised subject to a budget constraint that takes
into account the "value" of the liquidity benefit associated with the money
supply. For any choice of the bivariate utility function, the resulting model
determines a relation between the rate of consumption, the price level, and the
money supply. The model also produces explicit expressions for the real and
nominal pricing kernels, and hence establishes a basis for the valuation of
inflation-linked securities.
