Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the...

Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and establish their existence. In general, such equilibria lead to Pareto inefficiency and coincide with Arrow-Debreu equilibria only if the values of net...

Risk parity has been considered a heuristic asset allocation method. In this paper, we show that, to the contrary, risk parity is a special case of a mean-risk type of a portfolio optimization problem with log-regularization to constrain weights. We show that log-regularization leads to a fund...

We show in a simple framework that momentum trading can exist in equilibrium and momentum trading is profitable. Properties of the model fit the empirics well. First, the model captures in a parsimonious manner both short-term overreaction and long-term reversals. Second, it predicts that...

We examine a production-based asset pricing model with an unobservable mean growth rate ollowing a two-state Markov chain and with an ambiguity averse representative agent. Our model requires a low coefficient of relative risk aversion to produce: (i) a high equity premium and volatile equity...

We study portfolio selection in a one-period financial market with an Expected Shortfall (ES) constraint. Unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation regulatory arbitrage and show that the presence or absence of...

To analyze the economic significance of pricing errors of stock index options, a system of linear inequalities is developed which completely characterizes all risk arbitrage opportunities which arise if a well-behaved pricing kernel does not exist. The Stochastic Arbitrage system can account for...

This paper explores the problem of an agent who invests in financial assets, works and/or accumulates human capital, and retires at the end of time horizon. His/her initial endowments consist of an amount of liquid assets (maybe because of inheritance) and a number of units of human...

We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure ρ on L1. We first show that under mild assumptions, the set of optimal portfolios for a fixed return is nonempty and compact. However, unlike in classical...

The optimal growth of a wealth process toward a goal is studied under ambiguous markets with first- and second-order moment uncertainties relating to stock returns. Optimal strategies and value functions are solved explicitly. A verification theorem is proved to show that the results solve the...