CLOSED-FORM SOLUTIONS FOR OPTIMAL PORTFOLIO SELECTION WITH STOCHASTIC INTEREST RATE AND INVESTMENT CONSTRAINTS

We examine the portfolio choice problem of an investor with constant relative risk aversion in a financial market with partially hedgeable interest rate risk. The individual shadow price of the portfolio constraint is characterized as the solution of a new backward equation involving Malliavin derivatives. A generalization of this equation is studied and solved in explicit form. This result, applied to our financial model, yields closed-form solutions for the shadow price and the optimal portfolio. The effects of parameters such as risk aversion, interest rate volatility, investment horizon, and tightness of the constraint are examined. Applications of our method to a monetary economy with inflation risk and to an international setting with currency risk are also provided.     

Heterogeneous preferences and equilibrium trading volume

The representative-agent Lucas model stresses aggregate risk and hence does not allow us to study the impact of agents’ heterogeneity on the dynamics of equilibrium trading volume. In this paper, we investigate under what conditions non-informational heterogeneity, i.e., differences in preferences and endowments, leads to nontrivial trading volume in equilibrium. We present a non-informational no-trade theorem that provides necessary and sufficient conditions for zero equilibrium trading volume in a continuous-time Lucas market model with heterogeneous agents, multiple goods, and multiple securities. We explain in detail how no-trade equilibria are related to autarky equilibria, portfolio autarky equilibria, and peculiar financial market equilibria, which play an important role in the literature on international risk sharing.     

A Monte Carlo Method for Optimal Portfolios

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.     

Asymptotic properties of Monte Carlo estimators of diffusion processes

This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. We examine two types of estimators based on the Euler scheme, one applied to the original processes, the other to a Doss transformation of the processes. We show that the transformation increases the speed of convergence of the Euler scheme. We also study estimators of conditional expectations of diffusions. After characterizing expected approximation errors, we construct second-order bias-corrected estimators. We also derive new convergence results for the Mihlstein scheme. Illustrations of the results are provided in the context of simulation-based estimation of diffusion processes.