This paper characterizes informed trade when speculators can acquire distinct signals of varying quality about an asset's value at different dates. The most reasonable characterization of private information about stocks is that while information is long‐lived, new information will arrive over time, information that may be acquired by others. Hence, while a speculator may know more than others at a moment, in the future, his information will become stale, but not valueless. In an environment that allows for arbitrary correlations among signals, we characterize equilibrium outcomes including trading, prices, and profits. We provide explicit numerical characterizations for different informational environments.

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 agent's 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.

We study a continuous‐time contracting problem under hidden action, where the principal has ambiguous beliefs about the project cash flows. The principal designs a robust contract that maximizes his utility under the worst‐case scenario subject to the agent's incentive and participation constraints. Robustness generates endogenous belief heterogeneity and induces a tradeoff between incentives and ambiguity sharing so that the incentive constraint does not always bind. We implement the optimal contract by cash reserves, debt, and equity. In addition to receiving ordinary dividends when cash reserves reach a threshold, outside equity holders also receive special dividends or inject cash in the cash reserves to hedge against model uncertainty and smooth dividends. The equity premium and the credit yield spread generated by ambiguity aversion are state dependent and high for distressed firms with low cash reserves.

We provide a theory of rational stock price bubbles in production economies with infinitely-lived agents. Firms meet stochastic investment opportunities and face endogenous credit constraints. They are not fully committed to repaying debt. Credit constraints are derived from incentive constraints in optimal contracts which ensure default never occurs in equilibrium. Stock price bubbles can emerge through a positive feedback loop mechanism and cannot be ruled out by transversality conditions. These bubbles command a liquidity premium and raise investment by raising the debt limit. Their collapse leads to a recession and a stock market crash.

This paper presents an infinite-horizon model of production economies in which firms face idiosyncratic productivity shocks and are subject to endogenous credit constraints. Credit-driven stock price bubbles can arise which can relax credit constraints and reallocate capital more efficiently among firms. The collapse of bubbles causes a fall of total factor productivity.

We study optimal control problems in the multivariate linear‐quadratic‐Gaussian framework under rational inattention. We propose a three‐step procedure to solve this problem using semidefinite programming and derive the optimal signal structure without strong prior restrictions. We analyze both the transition dynamics of the optimal posterior covariance matrix and its steady state. We characterize the optimal information structure for some special cases and develop numerical algorithms for general cases. Applying our methods to solve three multivariate economic models, we obtain some results qualitatively different from the literature.