Canada's Approach to Financial Regulation

This paper discusses aspects of designing appropriate financial regulation for Canada. It outlines a theory of financial system organization and uses it to assess recent legislative actions and proposals. The paper argues that current and proposed regulation incorporates too many constraints and does not provide for sufficient information dissemination. Nor does it in all cases provide appropriate incentives for improved system functioning.

The Stochastic Cash Balance Problem with Fixed Costs for Increases and Decreases

The stochastic cash balance problem is an inventory problem in which the stochastic cash (or inventory) change can either be positive or nonpositive, and in which decisions to increase or decrease the inventory are permitted at the beginning of each time period. The paper studies problems in which both fixed and proportional costs can be incurred whenever the inventory is changed in either direction. An example is used to demonstrate that when these costs are positive and the loss function is convex, a simple policy (analogous to a two-sided (s, S) policy) is not generally optimal. The example is also used to display the relations between the cash balance problem and inventory problems previously studied by Scarf and Veinott. When proportional costs of changing the inventory are zero, the two fixed costs are equal, the loss function is symmetric quasi-convex, and the problem's probability densities are quasi-concave a simple policy is shown to be optimal. For the cases in which simple policies are not optimal, the paper develops a technique which employs convex upper and lower bounds on the (nonconvex) cost functions partially to describe the optimal policy. It is suggested that this convex bounding technique may provide an approach to studying the cost implications of following simple, nonoptimal policies in inventory problems for which the optimal policy is complex.

Dominance Relations Among Standardized Variable

This paper examines stochastic dominance relations among discrete random variables defined on a common integer domain. While these restrictions are minimal, they lead both to new theoretical results and to simpler proofs of existing ones. The new results, obtained for dominance criteria of any degree, generalize an SSD result of Rothschild -Stiglitz to describe how for any dominance criterion a dominated variable is equal in distribution to a dominated variable plus perturbation terms. If the variables are comparable under FSD the perturbations are downward shift terms, while under SSD (TSD) all but two (three) of the perturbations are zero mean disturbance terms (noise). Under SSD the remaining perturbations are shift terms and under TSD noise and shift terms. However, under either SSD or TSD these remaining terms are identically zero if the variables to be compared have equal means. The paper also finds new proofs of well known results relating dominance criteria to preference

Standardized Variables, Risks and Preference

This paper examines the expected utility effects of adding one risk to another. In comparison to related works, it places fewer restrictions on utilities and more structure on risky asset returns. The paper, entailing little loss of generality, uses discrete variables defined on a common domain (hereafter standardized variables) to find sufficient conditions for either of two (dependent or independent) variables to dominate their sum in the second degree. It then finds (higher order) sufficient conditions for either of the variables to dominate their sum in the third degree. While utilities are only restricted to be increasing concave, the expected utility differences for the respective risk positions are the same as if the investors were respectively proper or standard risk averse (Pratt-Zeckhauser [1987], Kimball [1993]

Standardized Variables and Optimal Risky Investment

This paper studies the optimal risky investment problem with fewer restrictions on utilities, and more structure on risks, than does the current literature. It uses discrete random variables defined on a common domain, hereafter called standardized variables, to obtain new results without important loss of generality. The optimal amount of investment in a single risky asset does not always decrease as risk increases in the Rothschild-Stiglitz ([1970, 1971]; hereafter RS) sense. However, by using standardized variables to define wealth dependent measures of risk and return, the paper finds necessary and sufficient conditions on risks such that an increase in risk does cause decreasing optimal risky investment. The paper thus complements the RS results. For investment in two risky assets, the paper uses standardized variables to find conditions on risks such that the riskier asset's demand to decrease (increase) as the Arrow-Pratt absolute risk aversion index increases (decreases), and thereby complements Ross' [1981] results