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We consider a general framework of optimal mechanism design under adverse selection and ambiguity about the type distribution of agents. We prove the existence of optimal mechanisms under minimal assumptions on the contract space and prove that centralized contracting implemented via mechanisms is equivalent to delegated contracting implemented via a contract menu under these assumptions. Our abstract existence results are applied to a series of applications that include models of optimal risk sharing and of optimal portfolio delegation., Literature review has been updated and expanded

Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing, we provide a new approach to asset pricing based on Backward Volterra equations. The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs. We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which, to the best of our knowledge, has not yet been studied. We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations. Finally, we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.

Any dynamic or stochastic notion of a general equilibrium relies on the underlying commodity space. Under sole risk and without multiple–prior uncertainty the usual choice is a Lebesgue space from standard measure theory. In the case of volatility uncertainty it turns out that such a type of function space is no longer appropriate. For this reason we introduce and discuss a new natural commodity space, which can be constructed in three independent and equivalent ways. Each approach departs from one possible way to construct Lebesgue spaces. Moreover, we give a complete representation of the resulting topological dual space. This extends the classic Riesz representation in a natural way. Elements therein are the candidates for a linear equilibrium price system. This representation result has direct implications for the microeconomic foundation of finance under Knightian uncertainty.

This article considers general equilibrium economies with a primitive uncertainty model that features ambiguity about continuous-time volatility. For the resulting non-equivalence of priors, an appropriate commodity-price space is introduced. Agents are heterogeneous in the size of captured ambiguity, endowment and preference for risk and ambiguity. Preferences are of variational type a la Maccheroni et al. (Econometrica 74(6):1447–1498, 2006). One important implication involves a problematic aspect of linear equilibrium price systems. Positive payoffs are for free on events outside the domain of the representing equilibrium pricing measure. Moreover, when aggregate risk is present and aggregate ambiguity is absent, the insurance properties of optimal allocations depend on the notion of ambiguity-free payoffs.

We study economies in which agents face Knightian uncertainty about state prices. Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such equilibria lead to Pareto inefficient allocations; the equilibria coincide with Arrow-Debreu equilibria only if the values of net trades are ambiguity-free in the mean. In economies without aggregate uncertainty, inefficiencies are generic. We introduce a constrained efficiency concept, uncertainty-neutral efficiency; equilibrium allocations under price uncertainty are efficient in this constrained sense. Arrow-Debreu equilibria turn out to be non-robust with respect to the introduction of Knightian uncertainty.

The α-maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of α. In this paper, we derive a recursive, dynamically consistent version of the α-maxmin model. In the continuous-time limit, the resulting dynamic utility function can be represented as a convex mixture between worst and best case, but now at the local, infinitesimal level.We study the properties of the utility function and provide an Arrow-Pratt approximation of the static and dynamic certainty equivalent. We derive a consumption-based capital asset pricing formula and study the implications for derivative valuation under indifference pricing.

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 equilibrium allocation are mean ambiguity-free.

The present paper considers a class of general equilibrium economies when the primitive uncertainty model features uncertainty about continuous-time volatility. This requires a set of mutually singular priors, which do not share the same null sets. For this setting we introduce an appropriate commodity space and the dual of linear and continuous price systems. All agents in the economy are heterogeneous in their preference for uncer- tainty. Each utility functional is of variational type. The existence of equi- librium is approached by a generalized excess utility fixed point argument. Such Arrow-Debreu allocations can be implemented into a Radner economy with continuous-time trading. Effective completeness of the market spaces al- ters to an endogenous property. Only mean unambiguous claims equivalently satisfying the classical martingale representation property build the marketed space.

This paper establishes, in the setting of Brownian information, a general equilibrium existence result in a heterogeneous agent economy. The existence is generic among income distributions. Agents differ moreover in their stochastic differential formulation of intertemporal recursive utility. The present class of utility functionals is generated by a recursive integral equation and incorporates preference for the local risk of the stochastic utility process. The setting contains models in which Knightian uncertainty is represented in terms of maxmin preferences of Chen and Epstein (Econometrica 70:1403-1443, 2002). Alternatively, Knightian decision making in terms of an inertia formulation from Bewley (Decis. Econ. Financ. 25:79-110, 2002) can be modeled as well.

The alpha-maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of alpha. In this paper, we derive a recursive, dynamically consistent version of the alpha-maxmin model. In the continuous-time limit, the resulting dynamic utility function can be represented as a convex mixture between worst and best case, but now at the local, infinitesimal level. We study the properties of the utility function and provide an Arrow-Pratt approximation of the static and dynamic certainty equivalent. We then derive a consumption-based capital asset pricing formula and study the implications for derivative valuation under indifference pricing.