One of the remarkable features of the mean-variance capital asset pricing model is its robustness with respect to changes in assumption (Jensen [1]). An example of this property is given by David Mayers [4], who shows that the structure of prices of marketable assets is unaffected by relaxing the assumption that all risky assets are marketable. The result has been used in the analysis of public sector investments by Stapleton and Subrahmanyam [6]. However, although relative prices are unaffected, the general level may be due to the effect of marketability on the market price of risk.

In this article, we characterize economies in which both cash flows and forward prices follow random walks. We show in the case of geometric random walks that the preferences of the representative investor are of the constant proportional risk-aversion type. We also show the conditions under which spot prices follow random walks and under which the equivalent martingale measure is non-state-dependent.

I. Introduction, 399.—II. Asset prices in a mixed economy, 401—III. Optimal levels of investment in a mixed economy, 403.—IV. Conclusion, 408.

ABSTRACT There are several examples in the literature of contingent claims whose payoffs depend on the outcomes of two or more stochastic variables. Familiar cases of such claims include options on a portfolio of options, options whose exercise price is stochastic, and options to exchange one asset for another. This paper derives risk neutral valuation relationships (RNVRs) in a discrete time setting that facilitate the pricing of such complex contingent claims in two specific cases: joint lognormally distributed underlying variables and constant proportional risk aversion on the part of investors, and joint normally distributed underlying variables and constant absolute risk aversion preferences, respectively. This methodology is then applied to the valuation of several interesting complex contingent claims such as multiperiod bonds, multicurrency option bonds, and investment options.

ABSTRACT This paper values options on assets whose returns, over a finite interval of time, are generated by a binomial process. It shows that a simple valuation relationship, between the option and the underlying stock, obtains if investors have preference functions that belong to a particular class, even if opportunities to hedge do not exist. One particular application of the theory is in the case where the stock price over a finite interval could increase by an amount, fall by the same amount, or stay at the same level. The results in this paper may be viewed as the foundation of the preference‐based approaches to obtaining a risk neutral valuation relationship.

ABSTRACT This note shows that a linear market model is sufficient to derive a linear relationship between beta and expected return. Furthermore, the slope of the relationship will be identical with that of the Capital Asset Pricing Model if the return on the market portfolio is normally distributed. However, results from characterization theory suggest that the linear market model assumption is close to that of multivariate normality.