[Analysis of absence of arbitrage normally ignores payoffs in states to which the agent assigns zero probability. We extend the fundamental theorem of asset pricing to the case of "no empty promises" in which the agent cannot promise arbitrarily large payments in some states. There is a superpositive pricing rule that can assign positive price to claims in zero probability states important to the market as well as assigning positive prices to claims in the states of positive probability. With continuous information arrival, no empty promises can be enforced by shutting down the agent's subsequent investments once wealth hits zero.]

Many models use noise trader risk and corresponding violations of the Law of One Price to explain pricing anomalies, but include a storage technology in perfectly elastic supply or unlimited asset liability. Storage allows aggregate consumption risk to differ from exogenous fundamental risk, but using aggregate consumption as a factor for asset returns can make noise trader risk superfluous. Using (i) limited asset liability and limited storage withdrawals, or (ii) an endogenous locally riskless interest rate eliminates violations of the Law of One Price. Our main results use only budget equations and market clearing, and require virtually no assumptions about behavior.

[The Black-Scholes-Merton option valuation method involves deriving and solving a partial differential equation (PDE). But this method can generate multiple values for an option. We provide new solutions for the Cox-Ingersoll-Ross (CIR) term structure model, the constant elasticity of variance (CEV) model, and the Heston stochastic volatility model. Multiple solutions reflect asset pricing bubbles, dominated investments, and (possibly infeasible) arbitrages. We provide conditions to rule out bubbles on underlying prices. If they are not satisfied, put-call parity might not hold, American calls have no optimal exercise policy, and lookback calls have infinite value. We clarify a longstanding conjecture of Cox, Ingersoll, and Ross.]

Analysis of absence of arbitrage normally ignores payoffs in states to which the agent assigns zero probability. We extend the fundamental theorem of asset pricing to the case of “no empty promises” in which the agent cannot promise arbitrarily large payments in some states. There is a superpositive pricing rule that can assign positive price to claims in zero probability states important to the market as well as assigning positive prices to claims in the states of positive probability. With continuous information arrival, no empty promises can be enforced by shutting down the agent's subsequent investments once wealth hits zero.

The Black-Scholes-Merton option valuation method involves deriving and solving a partial differential equation (PDE). But this method can generate multiple values for an option. We provide new solutions for the Cox-Ingersoll-Ross (CIR) term structure model, the constant elasticity of variance (CEV) model, and the Heston stochastic volatility model. Multiple solutions reflect asset pricing bubbles, dominated investments, and (possibly infeasible) arbitrages. We provide conditions to rule out bubbles on underlying prices. If they are not satisfied, put-call parity might not hold, American calls have no optimal exercise policy, and lookback calls have infinite value. We clarify a longstanding conjecture of Cox, Ingersoll, and Ross.

We analyze competition among informed traders in the continuous‐time Kyle(1985) model, as Foster and Viswanathan (1996) do in discrete time. We explicitly describe the unique linear equilibrium when signals are imperfectly correlated and confirm the conjecture of Holden and Subrahmanyam (1992) that there is no linear equilibrium when signals are perfectly correlated. One result is that at some date, and at all dates thereafter, the market would have been more informationally efficient had there been a monopolist informed trader instead of competing traders. The relatively large amount of private information remaining near the end of trading causes the market to approach complete illiquidity.