We examine intertemporal asset pricing when short sales are constrained in proportion to the value of an investor’s portfolio. All assets’ prices exceed every investor’s marginal utility of consumption-based valuation of the associated dividends if every investor finds himself constrained in some asset in some state; we exhibit such an equilibrium. An asset’s price decomposes into three (investor-specific) components: the consumption value of its dividends, a speculative value premium, and a collateral value premium. The validity of the no-arbitrage pricing approach is shown to depend critically on the difference between real securities and their synthetic counterparts.

We develop lower and upper bounds on the prices of American call and put options written on a dividend-paying asset. We provide two option price approximations, one based on the lower bound (termed LBA) and one based on both bounds (termed LUBA). The LUBA approximation has an average accuracy comparable to a 1,000-step binomial tree with a computation speed comparable to a 50-step binomial tree. We introduce a modification of the binomial method (termed BBSR) that is very simple to implement and performs remarkably well. We also conduct a careful large-scale evaluation of many recent methods for computing American option prices.

This article addresses the problem of valuing American call options with caps on dividend-paying assets. Since early exercise is allowed, the valuation problem requires the determination of optimal exercise policies. Options with two types of caps are analyzed: constant caps and caps with a constant growth rate. For constant caps, it is optimal to exercise at the first time at which the underlying asset’s price equals or exceeds the minimum of the cap and the optimal exercise boundary for the corresponding uncapped option. For caps that grow at a constant rate, the optimal exercise strategy can be specified by three endogenous parameters.

This paper analyzes an economy in which investors operate under partial information about technology‐relevant state variables. It is shown that for Gaussian information structures under incomplete observations, the consumer's problem can be transformed into an equivalent program with a completely observed state: the conditional expectation of the underlying unobservable state variables. A consequence of this transformation is that classic results in finance remain valid under an appropriate reinterpretation of the state variables.

This paper analyzes asset prices in a representative agent exchange economy with habit-forming preferences. For a general class of utility indices and endowment processes, the authors characterize the optimal demand for consumption and derive explicit solutions for the interest rate and asset risk premia. They show that consumption smoothness may obtain even when the interest rate is stochastic. The consumption capital asset pricing model may not hold when the endowment process has stochastic coefficients; asset risk premia are larger under mild assumptions. The interest rate depends on the growth in the standard of living. Malliavin calculus is employed in the analysis.

In this paper, we focus on the optimal demand for futures contracts by an investor with a logarithmic utility function who attempts to hedge a nontraded cash position. When the analysis is conducted in the “cash‐commodity‐price” space, we show that the value function associated with the Bernoulli investor program is not additively separable, thus suggesting that this investor hedges against shifts in the opportunity set as represented by the commodity price. By establishing the equivalence between the cash formulation of the problem and the wealth formulation, we are able to analyze the problem in the “wealth‐commodity‐price” space. In this space, we show the additive separability of the value function when the futures settlement price process is perfectly locally correlated with the commodity price process. The demand for futures in this instance is composed of (a) a mean‐variance term and (b) a minimum‐variance component that is a classic feature of models with nontraded assets. Since the first‐best (nonmyopic) optimum is attained, however, the deviation from a mean‐variance demand should not be interpreted as the expression of a nonmyopic behavior but rather as an attempt to restore a first‐best optimum. On the other hand, when the correlation between the futures price and the underlying commodity price is imperfect, in general, the value function does not separate additively, the first‐best solution cannot be attained, and the optimal futures trading strategy involves a hedging term against shifts in the opportunity set.

In this paper, we focus on the optimal demand for futures contracts by an investor with a logarithmic utility function who attempts to hedge a nontraded cash position. When the analysis is conducted in the “cash-commodity-price” space, we show that the value function associated with the Bernoulli investor program is not additively separable, thus suggesting that this investor hedges against shifts in the opportunity set as represented by the commodity price. By establishing the equivalence between the cash formulation of the problem and the wealth formulation, we are able to analyze the problem in the “wealth-commodity-price” space. In this space, we show the additive separability of the value function when the futures settlement price process is perfectly locally correlated with the commodity price process. The demand for futures in this instance is composed of (a) a mean-variance term and (b) a minimum-variance component that is a classic feature of models with nontraded assets. Since the first-best (nonmyopic) optimum is attained, however, the deviation from a mean-variance demand should not be interpreted as the expression of a nonmyopic behavior but rather as an attempt to restore a first-best optimum. On the other hand, when the correlation between the futures price and the underlying commodity price is imperfect, in general, the value function does not separate additively, the first-best solution cannot be attained, and the optimal futures trading strategy involves a hedging term against shifts in the opportunity set.

We study investments in exclusive projects with different cost structures. Our analysis incorporates the possibility of producing a stochastic revenue stream from two alternative technologies with a stochastic variable cost and a fixed cost, respectively, and accounts for project managers’ endogenous operating decisions. The optimal investment decision is characterized by two possibly nonmonotone boundaries. We examine the effect of operating leverage on managerial policies, investment decisions, and values and carry out an application to power generation projects. We assess the impact of knowledge acquisition, that is, investments in growth options.

This paper derives and analyzes dynamic timing strategies of a fund manager with private information. Endogenous timing strategies generated by various information structures and skills, and associated fund styles, are identified. Endogenous fund returns are characterized in the public information of an uninformed observer. Timing components are identified. The paper provides foundations for regression analyses of fund returns and tests of market timing.

A new decomposition of the optimal portfolio, in dynamic models with von Neumann–Morgenstern preferences and Ito prices, is established. The formula rests on a change of numéraire that uses pure discount bonds as units of account. The dynamic hedging demand has two components. The first hedge insures against fluctuations in an optimally designed bond with a maturity date matching the investor's horizon. The second hedge immunizes against fluctuations in the market price of risk in the bond numéraire. Various applications are examined. New results concerning the behavior of extremely risk-averse individuals, the demand for bonds and its long-horizon limit, and the optimal portfolio in incomplete markets are derived.