[This paper presents an implicit-contract model in which workers are allowed to differ in both their productive abilities and their preferences. It is shown that if firms are able to vary hours costlessly among their workers, workers are risk averse, and there are no outside payments to laid-off workers, then efficient contracts between firms and their workers will never provide for layoff unemployment. If, however, such hours variations are not costless, layoffs are no longer generally inefficient since they are an alternative means by which firms can adjust the labor inputs of selected groups of workers.]

We examine the optimal trading strategy for a CRRA investor who maximizes the expected utility of wealth on a finite date and faces transaction costs. Closed-form solutions are obtained when this date is uncertain. We then show a sequence of analytical solutions converge to the solution to the problem with a deterministic finite horizon. Consistent with the common life-cycle investment advice, the optimal trading strategy is found to be horizon dependent and largely buy and hold. Moreover, it might be optimal for the investor in our model not to buy any stock, even when the risk premium is positive. Further analysis of the optimal policy is also provided.

Data from the National Longitudinal Survey of Youth indicate that the employer often pays the explicit costs of not only on‐site training but also off‐site general training. Although few of these costs appear to be passed on to workers in the form of a lower wage while in training, completed spells of general training paid for by previous employers have a larger wage effect than completed spells of general training paid for by the current employer. A model where contract enforcement considerations cause employers to share the costs and returns to purely general training can explain these findings.

Reload options, call options granting new options on exercise, are popularly used in compensation. Although the compound option feature may seem complicated, there is a distribution-free dominant policy of exercising reload options whenever they are in the money. The optimal policy implies general formulas for numerical valuation. Simpler formulas for valuation and hedging follow from Black-Scholes assumptions with or without continuous dividends. Time vesting affects the optimal policy, but numerical results indicate that it is nearly optimal to exercise in the money whenever feasible. The results suggest that reload options produce similar incentives as employee stock options and share grants.

ABSTRACT Many models use noise trader risk and corresponding violations of the Law of One Price to explain pricing anomalies, but include a storage technology in perfectly elastic supply or unlimited asset liability. Storage allows aggregate consumption risk to differ from exogenous fundamental risk, but using aggregate consumption as a factor for asset returns can make noise trader risk superfluous. Using (i) limited asset liability and limited storage withdrawals, or (ii) an endogenous locally riskless interest rate eliminates violations of the Law of One Price. Our main results use only budget equations and market clearing, and require virtually no assumptions about behavior.

An employer must choose a procedure for screening job applicants, a rate of hire, a training program for new employees, a criterion for the retention of new employees after observing their on-the-job performance, a compensation package, and a rate of capital investment so as to minimize production costs across time. This paper examines the effects of employer size on these hiring and training decisions when larger employers have greater monitoring costs. A unique data set is employed to estimate the empirical relation among employer size and employer search, training, capital investment, and wages.

Conventional analysis predicts that workers pay part of their on-the-job training costs by accepting a lower starting wage and subsequently realize a return to this investment in the form of greater wage growth. Missing from the conventional treatment of on-the-job training is a discussion of the process by which heterogeneous workers are matched to jobs requiring varying amounts of training. This matching process constitutes a key feature of the on-the-job training model presented in this article and tested with a unique data set containing extensive information concerning on-the-job training, employer search, wages, and wage and productivity growth.

Abstract Financial transaction taxes, or generally transaction costs, are salient in derivatives markets and seldom studied in equilibrium models. We study a tractable model with proportional transaction costs where agents trade a derivative with nonlinear payoffs to hedge nontraded endowments. We show that trade is sustained in an equilibrium with transaction costs only if there is sufficient heterogeneity in risk aversion. When there is trade, the equilibrium return variance increases in transaction costs. These results are driven by how mean-variance demands, hedging demands, and asymmetry of no-transaction region widths determine the equilibrium Sharpe ratio and return volatility when transaction costs change.

[The Black-Scholes-Merton option valuation method involves deriving and solving a partial differential equation (PDE). But this method can generate multiple values for an option. We provide new solutions for the Cox-Ingersoll-Ross (CIR) term structure model, the constant elasticity of variance (CEV) model, and the Heston stochastic volatility model. Multiple solutions reflect asset pricing bubbles, dominated investments, and (possibly infeasible) arbitrages. We provide conditions to rule out bubbles on underlying prices. If they are not satisfied, put-call parity might not hold, American calls have no optimal exercise policy, and lookback calls have infinite value. We clarify a longstanding conjecture of Cox, Ingersoll, and Ross.]

We examine the optimal trading strategy for a CRRA investor who maximizes the expected utility of wealth on a finite date and faces transaction costs. Closed-form solutions are obtained when this date is uncertain. We then show a sequence of analytical solutions converge to the solution to the problem with a deterministic finite horizon. Consistent with the common life-cycle investment advice, the optimal trading strategy is found to be horizon dependent and largely buy and hold. Moreover, it might be optimal for the investor in our model not to buy any stock, even when the risk premium is positive. Further analysis of the optimal policy is also provided.