Jianjun Miao

A Two-Person Dynamic Equilibrium under Ambiguity

This paper describes a pure-exchange, continuous-time economy with two heterogeneous agents and complete markets. A novel feature of the economy is that agents perceive some security returns as ambiguous in the sense often attributed to frank Knight. The equilibrium is described completely in closed-form. In particular, closed-form solutions are obtained for the equilibrium processes describing individual consumption, the interest rate, the market price of uncertainty, security prices and trading strategies. After identifying agents as countries, the model is applied to address the consumption home-bias puzzles.

Irreversible Investment with Regime Shifts

Under the real options approach to investment under uncertainty, agents formulate optimal policies under the assumption that firms’ growth prospects do not vary over time. This paper proposes and solves a model of investment decisions in which the growth rate and volatility of the decision variable shift between different states at random times. A value-maximizing investment policy is derived such that in each regime the firms investment policy is optimal and recognizes the possibility of a regime shift. Under this policy, investment is intermittent and increases with marginal q. Moreover, investment typically is very small but, in some states, the capital stock jumps. Implications for marginal q and the user cost of capital are also examined.

Investment, Consumption, and Hedging Under Incomplete Markets

Entrepreneurs often face undiversifiable idiosyncratic risks from their business investments. We extend the standard real options approach to an incomplete markets environment and analyze the joint decisions of business investments, consumption/savings, and portfolio selection. For a lump-sum investment payoff and an agent with a sufficiently strong precautionary savings motive, an increase in volatility can accelerate investment, contrary to the standard real options analysis. When the agent can trade the market portfolio to partially hedge against investment risk, the systematic volatility is compensated via the standard CAPM argument, and the idiosyncratic volatility generates a private equity premium. Finally, when the investment payoff is a series of flows, the agents idiosyncratic risk exposure alters both the implied option value and the implied project value, causing a reversal of the results in the lump-sum payoff case.

Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks

This paper studies competitive equilibria of a production economy with aggregate productivity shocks. There is a continuum of consumers who face borrowing constraints and individual labor endowment shocks. The dynamic economy is described in terms of sequences of aggregate distributions. The existence of sequential competitive equilibria is proven and a recursive characterization is established. In particular, it is shown that for any sequential competitive equilibrium, there exists a payoff equivalent sequential competitive equilibrium that is generated by a suitably defined recursive equilibrium with state variables including continuation value.

Bubbles and Credit Constraints

We provide an infinite-horizon model of a production economy with credit-driven stock- price bubbles, in which firms meet stochastic investment opportunities and face credit constraints. Capital is not only an input for production, but also serves as collateral. We show that bubbles on this reproducible asset may arise, which relax collateral constraints and improve investment efficiency. The collapse of bubbles leads to a recession and a stock market crash. We show that there is a credit policy that can eliminate the bubble on firm assets and can achieve the efficient allocation.

Intertemporal substitution and recursive smooth ambiguity preferences

In this paper, we establish an axiomatically founded generalized recursive smooth ambiguity model that allows for a separation among intertemporal substitution, risk aversion, and ambiguity aversion. We axiomatize this model using two approaches: the second-order act approach a la Klibanoff et al. (2005) and the twostage randomization approach a la Seo (2009). We characterize risk attitude and ambiguity attitude within these two approaches. We then discuss our model’s application in asset pricing. Our recursive preference model nests some popular models in the literature as special cases.

Risk, uncertainty, and option exercise

Many economic decisions can be described as an option exercise or optimal stopping problem under uncertainty. Motivated by experimental evidence such as the Ellsberg Paradox, we follow Knight (1921) and distinguish risk from uncertainty. To capture this distinction, we adopt the multiple-priors utility model. We show that the impact of ambiguity on the option exercise decision depends on the relative degrees of ambiguity about continuation payoffs and termination payoffs. Consequently, ambiguity may accelerate or delay option exercise. We apply our results to investment and exit problems, and show that the myopic NPV rule can be optimal for an agent having an extremely high degree of ambiguity aversion.

Dynamic Asset Allocation with Ambiguous Return Predictability

We study an investors optimal consumption and portfolio choice problem when he confronts with two possibly misspecified submodels of stock returns: one with IID returns and the other with predictability. We adopt a generalized recursive ambiguity model to accommodate the investors aversion to model uncertainty. The investor deals with specification doubts by slanting his beliefs about submodels of returns pessimistically, causing his investment strategy to be more conservative than the Bayesian strategy. This effect is large for extreme values of the predictive variable. Unlike in the Bayesian framework, model uncertainty induces a hedging demand, which may cause the investor to decrease his stock allocations sharply and then increase with his prior probability of IID returns. Adopting suboptimal investment strategies by ignoring model uncertainty can lead to sizable welfare costs.

NUMERICAL SIMULATION OF NONOPTIMAL DYNAMIC EQUILIBRIUM MODELS

In this article, we propose a recursive equilibrium algorithm for the numerical simulation of nonoptimal dynamic economies. This algorithm builds upon a convergent operator over an expanded set of state variables. The fixed point of this operator defines the set of all Markovian equilibria. We study approximation properties of the operator. We also apply our recursive equilibrium algorithm to various models with heterogeneous agents, incomplete financial markets, endogenous and exogenous borrowing constraints, taxes, and money.

Advance information and asset prices

This paper provides a dynamic rational expectations equilibrium model in which investors have heterogeneous information and investment opportunities. Informed investors privately receive advance information about future earnings that is unrelated to current earnings. In response to good advance information, stock prices increase and informed investors act as trend chasers, increasing their investment in stocks. Informed investors also buy other investment opportunities that are positively correlated with stocks, bearing more aggregate risk. The expected risk premium increases generating short-run momentum. Uninformed investors sell stocks, acting as contrarians. When the advance information materializes in the future, excess returns fall, generating long-run reversals.