Preservation of “more risk averse” under expectations

The preservation of risk aversion properties of utility functions under expectation operations is of interest in the study of derived utility functions in sequential decision problems and in problems with multiple (contemporaneous) sources of uncertainty. The purpose of this note is to present sufficient conditions for the Pratt relation “more risk averse” to be preserved under expectations.     

Spanning and completeness with options

The role of ordinary options in facilitating the completionof securities markets is examined in the context of a modelof contigent claims sufficiently general to accommodate thecontinuous distributions of asset pricing theory and optionpricing theory. In this context, it is shown that call optionswritten on a single security approximately span all contingentclaims written on this security and that call options writtenon portfolios of call options on individual primitive securitiesapproximately span all contingent claims that can be writtenon these primitive securities. In the case of simple options,explicit formulas are given for the approximating options andportfolios of options. These results are applied to the pricingof contingent claims by arbitrage and to irrelevance propositionsin corporate finance.     

Operating efficiency and output insensitive employment contracts for capital management

Summary This paper considers a problem in which an agent is hired to manage a capital investment and subsequently receives private information regarding the productivity of the capital investment. The capital manager must decide whether to invest capital supplied by the firm (the principal), or to divert these investment funds to perquisite consumption. If the manager decides to invest, the manager must then select the level of operating efficiency (productivity) of the capital investment, this latter choice being unobservable and constrained by the (maximal) productivity of the investment. In this setting we demonstrate that the optimal employment contract, from the perspective of the firm hiring the manager, is the contract whichminimizes the dependence of the manager's compensation on firm output. This contract pays the manager a fixed wage whenever output from the investment exceeds the wage and provides the manager with all of the projects rents whenever output falls below this level. Thus, we provide a setting in which fixed wage contracts are the optimal incentive contract even when agents are risk neutral and contracts can be costlessly written on future output.We would like to thank the participants in the Princeton Economics and Finance Workshop and the Ohio State University Finance Workshop for their comments on an earlier draft of this paper. The second author gratefully acknowledges the research support of the Georgia State College of Business Administration Research Council.     

On the theory of risk aversion and the theory of risk

Relationships between the theory of risk aversion and the theory of risk have been noted by Diamond and Stiglitz [12], Kihlstrom and Mirman [24], and Leland [29]. The main result of this paper is a characterization of the Pratt and Kihlstrom-Mirman [24, 46] relation “more risk averse” between utility functions in terms of a stochastic dominance or “riskier” relation between certain probability measures derived from these utility functions. This result is used in the comparison of risk-adjusted portfolio yields to extend to the several risky asset case the intuition provided by the Arrow-Pratt [1, 46] portfolio theorem that “more risk averse” means “will take less risk.”     

Optimal design of securities under asymmetric information

A firm must decide what security to sell to raise external capitalto finance a profitable investment opportunity. There is exante asymmetry of information regarding the probability distributionof cashflow generated by the investment. In this setting, wederive necessary and sufficient conditions for a security tobe optimal (uniquely optimal), that is, for pooling at thissecurity to be an (the unique) equilibrium outcome. Using theseconditions we show that the debt contract is (uniquely) optimalif and only if cash flows are ordered by (strict) conditionalstochastic dominance. Finally, we derive an equivalence relationshipbetween optimal security designs and designs that minimize mispricing.     

Risk aversion,impatience, and optimal timing decisions

In this paper, a theory measuring a decision maker's aversion to temporal risks is developed in the context of a simple choice framework that admits the interpretation “time varying utility of wealth.” A relation “more temporally risk averse” is defined and characterized in terms of instantaneous risk aversion (the usual single variable case) and impatience. A further characterization of this relation is obtained in the context of a class of action timing problems known as optimal stopping problems and is applied to preference based investigations of information production, incentives to innovate, and job search.