We provide a simple binomial framework to value American-style derivatives subject to trading restrictions. The optimal investment of liquid wealth is solved simultaneously with the early exercise decision of the nontraded derivative. No-short-sales constraints on the underlying asset manifest themselves in the form of an implicit dividend yield in the risk-neutralized process for the underlying asset. One consequence is that American call options may be optimally exercised prior to maturity even when the underlying asset pays no dividends. Applications to executive stock options (ESO) are presented: it is shown that the value of an ESO could be substantially lower than that computed using the Black–Scholes model. We also analyze nontraded payoffs based on a price that is imperfectly correlated with the price of a traded asset.

This paper compares two recent Monte Carlo methods advocated for the computation of optimal portfolio rules. The candidate methods are the approach based on Monte Carlo with Malliavin Derivatives (MCMD) proposed by Detemple, Garcia and Rindisbacher [Detemple et al., 2003. A Monte-Carlo method for optimal portfolios. Journal of Finance 58, 401–406] and the approach based on Monte Carlo with regression (MCR) of Brandt, Goyal, Santa-Clara and Stroud [Brandt et al., 2003. A simulation approach to dynamic portfolio choice with an application to learning about return predictability. Working paper, Wharton School]. Our comparisons are carried out in the context of various intertemporal portfolio choice problems with two assets, a risky asset and a riskless asset, and different configurations of the state variables. The specifications studied include a linear model with a single state variable admitting an exact solution and a non-linear model with two state variables that requires a purely numerical resolution. The accuracies of the candidate methods are compared. We provide, in particular, efficiency plots displaying the speed–accuracy trade-off for various selections of the relevant simulation and discretization parameters. MCMD is shown to dominate in all the settings considered.

This paper studies equilibrium in a pure exchange economy with unobservable Markov switching growth regimes and beliefs-dependent risk aversion (BDRA). Risk aversion is stochastic and depends nonlinearly on consumption and beliefs. Equilibrium is obtained in closed form. The market price of risk, the interest rate, and the stock return volatility acquire new components tied to fluctuations in beliefs. A three-regime specification is estimated using the generalized method of moments (GMM). Model moments match their empirical counterparts for a variety of unconditional moments, including the equity premium, stock returns volatility, and the correlations between stock returns and consumption and dividends. Dynamic features of the data, such as the countercyclical behaviors of the equity premium and volatility, are also captured. Model volatility provides a good fit for realized volatility. A new factor, the information risk premium, is found to be a strong predictor of future excess returns. These results are obtained with an estimated risk aversion fluctuating between 1.44 and 1.93.

This paper proposes a new simulation‐based approach for optimal portfolio allocation in realistic environments with complex dynamics for the state variables and large numbers of factors and assets. A first illustration involves a choice between equity and cash with nonlinear interest rate and market price of risk dynamics. Intertemporal hedging demands significantly increase the demand for stocks and exhibit low volatility. We then analyze settings where stock returns are also predicted by dividend yields and where investors have wealth‐dependent relative risk aversion. Large‐scale problems with many assets, including the Nasdaq, SP500, bonds, and cash, are also examined.

We study equilibria in multi‐asset and multi‐agent continuous‐time economies with asymmetric information and bounded rational noise traders. We establish the existence of two equilibria. First, a full communication equilibrium where the informed agents' signal is disclosed to the market and static policies are optimal. Second, a partial communication equilibrium where the signal disclosed is affine in the informed and noise traders' signals, and dynamic policies are optimal. Here, information asymmetry creates demand for two public funds, as well as a dark pool where private information trades can be implemented. Markets are endogenously complete and equilibrium returns have a three factor structure with stochastic factors and loadings. Results are valid for constant absolute risk averse investors, general vector diffusions for fundamentals, nonlinear terminal payoffs, and non‐Gaussian noise trading. Asset price dynamics and public information flows are endogenous, and rational expectations equilibria are special cases of the general results.