Algebraic Geometry and Number Theory

A Course in Computational Algebraic Number Theory

THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]

Algebraic Geometry

Algebraic Graph Theory

String theory and noncommutative geometry

Commutative algebra with a view toward algebraic geometry

The algebraic theory of semigroups

A classical introduction to modern number theory

Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy

Introduction to Analytic Number Theory

A Mathematical Theory of Communication

Theory of the firm: Managerial behavior, agency costs and ownership structure

The theory of planned behavior

Self-efficacy: Toward a unifying theory of behavioral change.

Social Foundations of Thought and Action: A Social Cognitive Theory

The Discovery of Grounded Theory: Strategies for Qualitative Research.

Belief, Attitude, Intention, and Behavior: An Introduction to Theory and Research

Prospect Theory: An Analysis of Decision under Risk

The Nature of Statistical Learning Theory

The Discovery of Grounded Theory; Strategies for Qualitative Research