Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

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The Theory of Industrial Organization

Martingales and stochastic integrals in the theory of continuous trading

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

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Lectu re Notes in Economics and Mathematical Systems

Part 1 Introduction: main themes bounded rationality, opportunism and structure of markets rational expectations the equilibrium model real and financial sectors of the economy. Part 2 Two-period finance economy - motivation and summary: characteristics of the finance economy contingent market equilibrium financial market equilibrium absence of arbitrage no-arbitrage equilibrium a basic property of incomplete markets constrained pareto optimality abstract approach - adjoint equations. Part 3 Two-period security pricing - motivation and summary: inner product, differential and gradient valuation of income streams representative agent analysis capital asset pricing model (CAPM). Part 4 Stochastic financial economy - motivation and summary: event-tree commodity space stochastic exchange economy stochastic financial markets absence of arbitrage complete and incomplete markets no-arbitrage equilibrium example of non-existence existence and optimality. Part 5 Information efficiency of security prices - motivation and summary: conditional expectation and martingale efficient markets under risk neutrality efficient markets with risk aversion. Part 6 Production in a finance economy - motivation and summary: characteristics of production economy sole proprietorships partnerships corporations. Part 7 Monetary economy - motivation and summary: real and nominal contracts monetary equilibrium non-neutrality of monetary policy optimal monetary policy indexing contracts.

Theory of incomplete markets

Portfolio selection with transactions costs

Stock market price/earnings ratios should be influenced by demography. Since demography is predictable, stock returns should be as well. We provide a simple stochastic OLG model with a cyclical structure which generates cyclical P/E ratios. We calibrate the model to roughly fit the cyclical features of historical P/E ratios.

Demography and the Long-Run Predictability of the Stock Market

THE SECULAR MOVEMENT OF the U.S. stock market in the postwar period has been characterized by three distinct twenty-year episodes of sustained increases or decreases in real stock prices: the bull market of 1945-66, the subsequent bear market of the 1970s and early 1980s, and the bull market of the middle and late 1980s and the 1990s. Explanations of the most recent and spectacular bull market have typically been based on several factors: (1) the advent of a "new economy" in which innovations create a permanently higher rate of economic growth and an accompanying increase in the intangible capital of the corporate sector; (2) the substantial increase in participation in the market; and the apparent decrease in risk aversion of the baby-boom generation. (3) Similar arguments, based on the "new economy" created by the technical innovations of the immediate postwar period and increased participation in the stock market, have also been used to justify the bull market of the 1950s. (4) The period of declining stock prices from 1966 to 1982 has spawned fewer rationales, as documented by the well-known paper by Franco Modigliani and Richard Cohn. (5) They argued that real earnings and interest rates could not account for the 50 percent decline in the real Standard and Poor's (S&P) index between 1966 and 1978, and they found themselves forced to conclude that the only explanation for the sustained decrease in stock prices was that investors, at least in the presence of unaccustomed and fluctuating inflation, are unable to free themselves from certain forms of money illusion and therefore look to the nominal rather than the real rate of interest when valuing equity. Although these explanations probably capture important elements underlying the behavior of stock prices in each of the three episodes, they cannot readily be pieced together to form a coherent explanation of the stock market over the whole sixty-year period. The idea motivating this paper is that demography is a common thread that might provide a single explanation for the alternating bull and bear markets over the whole postwar period. Since the turn of the twentieth century, live births in the United States have also gone through alternating twenty-year periods of boom and bust: for example, the low birth rate during the Great Depression and the war years was followed by the baby boom of the 1950s and early 1960s and the baby bust of the 1970s. These birth waves have resulted in systematic changes in the age composition of the population over the postwar period, roughly corresponding to the twenty-year periods of boom and bust in the stock market. People have distinct financial needs at different periods of their life, typically borrowing when young, investing for retirement when middle-aged, and disinvesting during retirement. Stocks (along with other assets such as real estate and bonds) are a vehicle for the savings of those preparing for their retirement. It seems plausible that a large middle-aged cohort seeking to save for retirement will push up the prices of these securities, and that prices will be depressed in periods when the middle-aged cohort is small. We find that this is indeed the case in the model we develop in this paper, regardless of whether economic agents are myopic or fully aware of demography and its implications. James Poterba has argued that, if agents were rational, they would anticipate any demography-induced rise in stock prices twenty years before it happened, bidding up prices at that time and thereby negating much of the effect of demographics on stock prices. (6) We show that, in our model, if agents are myopic, blindly plowing savings into stocks when middle-aged, stock prices will be proportional to the size of the middle-aged cohort. But we also show that, when agents fully anticipate demographic trends, their rational response actually reinforces the effect on stock prices, making prices rise more than proportionally to the growth of the middle-aged cohort. …

/pdf/demography-and-the-long-run-predictability-of-the-stock-1cb93qvqmz.pdf

This paper extends the general equilibrium model with incomplete markets to an open-ended future, thereby providing a natural setting for analyzing problems in macroeconomics. Two concepts of equilibrium are defined that prevent agents from entering into Ponzi schemes: the first is based on debt constraints and the second is based on a transversality condition that limits the rate of growth of debt. Under the assumption that agents are impatient (Mackey continuity of preferences) and have a degree of impatience that is bounded below, the two concepts of equilibrium are shown to coincide and lead to existence of equilibrium. Copyright 1994 by The Econometric Society. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (T (This abstract was borrowed from another version of this item.)

Michael Magill

Papers

Theory of incomplete markets

Portfolio selection with transactions costs

Demography and the Long-Run Predictability of the Stock Market

Demography and the Long-Run Predictability of the Stock Market

Infinite Horizon Incomplete Markets