This paper values a contingent claim to discrete stochastic cash flows generated by a Poisson arrival process with a randomly varying intensity parameter. In the most general case, both the size and the arrival intensity of cash flows may correlate wih state variables in a continuous time economy. Assuming the conditions of an intertemporal capital aset pricing model, solutions for the value of the contingent claim can be found using various techniques. The paper suggests immediate applications to the valuation of insurance contracts, the decision to build a firm with unknown future investment opportunities, and the pricing of mortgage-backed securities.