The Valuation of Stochastic Cash Flows

A stochastic cash flow depends on a random outcome. Since insurance and reinsurance contracts in exchange for financial considerations provide financial compensations against random outcomes, their compensations are perfect examples of stochastic cash flows. This paper develops a theory for the valuation of such cash flows from the four principles of present value, utility, optimum, and equilibrium. The most important implication of the theory are that they optimal amount for an economic agent to purchase depends on price, that (price, amount) loci are preliminary to market value, and that market value is the unique price at which all interested economic agents purchase optimal amounts. The theory belies the prevalent practices of risk-adjusted discounting and capital allocation (Appendix A), faulting them for naïve and erroneous conceptions of time. Accordingly, although the information that the theory presumes of economic agents is formidable, each agent is realistically burdened with ascertaining its own present options and preferences, rather than impossibly burdened with omniscience. And it sets the agents to the virtuous task of extracting value from projects, rather than from one another. The theory lays claim to fundamental principles of financial economics; it derives from the work of European risk theorists Karl Borch, Hans Buhlmann, and Hans Gerber, and gains support from a small but growing number of American actuaries. Though the paper remains theoretical throughout (especially in Appendices B-D), it furnishes several examples of sufficient detail for actuaries to apply it to pricing traditional insurance and reinsurance contracts.