<p>This paper studies asset pricing when a stochastic discount factor can be represented as a weighted integral of a non-negative second order random field. The random field is used to construct a Hilbert space of random variables such that an asset’s expected excess payoff, which depends on the covariance between the asset’s payoff and the stochastic discount factor, is an inner product in the constructed Hilbert space. This Hilbert space is isometrically isomorphic to a reproducing kernel Hilbert space, where the reproducing kernel is the covariance kernel of the random field. Thus, an asset’s expected excess payoff can also be calculated as an inner product in the reproducing kernel Hilbert space. By working in the reproducing kernel Hilbert space, methods from mathematical learning theory can be used to study asset pricing. In this case, the reproducing kernel is the main input for asset pricing. Several examples are used to illustrate the technique.</p>