The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case of Merton-type formula is shown to result, provided jump probabilities are replaced by their corresponding Arrow-Debreu prices.

This paper develops a model for interdependent demand for health insurance and health care under uncertainty to throw light on the issue of insurance-induced distortions in the demand for health care services. The model is used to empirically analyse the determinants of the choice of health insurance type and seven types of health care services using micro-level data from the 1977–78 Australian Health Survey. Econometric implementation of the model involves, simultaneously, issues of discreteness of choice, selectivity and stochastic dependence between health insurance and utilization. Health status appears to be more important in determining health care service use than health insurance choice, while income appears to be more important in determining health insurance choice than in determining health care service use. For a broad range of health care services both moral hazard and self selection are found to be important determinants of utilization of health care services.