Scott F. Richard

Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model

Abstract A continuous time model for optimal consumption, portfolio and life insurance rules, for an investor with an arbitrary but known distribution of lifetime, is derived as a generalization of the model by Merton (1971). The classic Tobin-Markowitz separation theorem obtains with the mutual funds being identical to those obtained under the assumption of certain lifetime. The investor is found to have a ‘human capital’ component of wealth, which is independent of his preferences and risky market opportunities and represents the certainty equivalent of his future net (wage) earnings. Explicit solutions, which are linear in wealth, are found for the investor with constant relative risk aversion.

A continuous time equilibrium model of forward prices and futures prices in a multigood economy

Abstract This paper is a theoretical investigation of equilibrium forward and futures prices. We construct a rational expectations model in continuous time of a multigood, identical consumer economy with constant stochastic returns to scale production. Using this model we find three main results. First, we find formulas for equilibrium forward, futures, discount bond, commodity bond and commodity option prices. Second, we show that a futures price is actually a forward price for the delivery of a random number of units of a good; the random number is the return earned from continuous reinvestment in instantaneously riskless bonds until maturity of the futures contract. Third, we find and interpret conditions under which normal backwardation or contango is found in forward or futures prices; these conditions reflect the usefulness of forward and futures contracts as consumption hedges.

An arbitrage model of the term structure of interest rates

Abstract A formula for the price of default-free discount bonds of all maturities is found using a Black- Scholes type of arbitrage model which is based on the assumption that a portfolio of three default-free discount bonds of distinct maturities can be managed to be a perfect substitute for any other default-free discount bond. The formula relates the price of bonds to the real rate of interest, the anticipated rate of inflation and the equilibrium prices of interest rate and inflation risks. Bond prices are shown to be the expected value of the sure nominal proceeds of the bond discounted to the present at a random discount rate. It is shown that the unbiased expectations hypothesis is in general inconsistent with this model.

A new approach to the existence of equilibria in vector lattices

Abstract Motivated by recent work of Huang and Kreps it is shown that the existence of a general equilibrium in an exchange economy whose commodity space is a vector lattice is guaranteed if (in addition to standard hypotheses) the price space is also a lattice. This is very weak in contrast with the usual requirement that the topology of the commodity space be locally solid (i.e., continuity of the lattice operations), a condition violated in models of Jones and of Huang and Kreps. The key to our proof is a disaggregated approach to the construction of supporting prices.

Proper preferences and quasi-concave utility functions

Abstract It is shown that preferences which are continuous, convex and uniformly proper [Mas-Colell (1983)] on the positive cone of a Banach lattice can be represented by a quasi-concave utility function which is defined on a larger domain with non-empty interior. This utility function may be chosen to be either upper or lower semi-continuous on its domain, and continuous at each point of the positive cone. Conversely, any preference relation on the positive cone which is monotone and arises from such a utility function is shown to satisfy a condition which is slightly weaker than uniform properness but which (in the presence of appropriate compactness assumptions) is sufficient to establish the existence of quasi-equilibria. An example is presented to illuminate the role played by the uniformity requirement.

A positive theory of in-kind transfers and the negative income tax

ConclusionNormative arguments for restricting redistribution to cash transfers or a negative income tax have not appealed to politicians or their constituents. All modern governments redistribute income in kind and provide goods and services that can be produced and distributed privately. At times public and private supply coexist. Housing services, medical care, and education are examples, but so too are safety and many regulatory activities of government.

Equilibrium in economies with infinitely many consumers and infinitely many commodities

Abstract This paper examines the existence of equilibrium in an economy with a countable infinity of consumers in which the commodity space is L ∞ . We prove the existence of a quasi-equilibrium when preferences are Mackey continuous. We also explore the relationship between equilibria and optima in the model.