In this paper, we apply the Laplace transform to risk preference theory (decision theory, decision analysis). We show that with a constant measure of absolute risk aversion, the certainty monetary equivalent (CME) can be developed into an expression involving the logarithm of the bilateral Laplace transform of the probability density of the outcome of risky projects. We also introduce a measure named internal risk aversion (IRA). This is in analogy with the earlier application of the transform to net present value problems. Properties of the CME function are examined. Basic examples of application are introduced followed by applications to portfolio theory and option pricing.