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Two models are developed for setting prices of new assets. One finds limits for pricing without arbitrage, and the other sets a minimum level where an investor would purchase the asset.

The value of the correlation pricing formula versus the capital assets pricing model, when determining asset prices, is discussed. The correlation pricing formula is useful in theoretical and practical applications.

A product representation technique featuring products of binomial trees for use in simultaneous management of several risky assets is presented and evaluated. The technique goes around the disproportional representation of products by presenting a condition of the marginal utility being optimally independent thus resulting in the proper defining of risk neutral probabilities in the product tree.

Two mutually dual optimization principles characterizing economic equilibria are described. The first, the zero-maximum principle, proposes that equilibrium allocations and allocations that maximize total societal benefit are equivalent and that the value of the benefit is zero. In contrast, the zero-minimum principle holds that equibrium price vectors and price vectors that minimize the total economic surplus are equivalent and that the value of this surplus is zero.

The relation between dual Pareto efficiency and equilibria in a framework that does not require differentiability is studied in an economy with d commodities and n individuals for assignments (p, M) where p is a price vector and M is a set of n individual income levels. The connection is explained by two theorems that are duals of the First and Second Theorems of Welfare Economics.

The criterion almost always proposed for evaluating investment portfolios is based on the expected logarithm of one-period return because it almost certainly lead to exponential growth. The inclusion of the variance of the logarithm of return is also suggested but this has not been substantially justified in theory. However, this log-variance criteria can be shown to naturally follow from elementary assumptions on an agent's preference relation for deterministic wealth sequences.