Arbitrage-free modeling under Knightian uncertainty

Viability and Arbitrage under Knightian Uncertainty

We reconsider the microeconomic foundations of financial economics under Knightian Uncertainty. In a general framework, we discuss the absence of arbitrage, its relation to economic viability, and the existence of suitable nonlinear pricing expectations. Classical financial markets under risk and no ambiguity are contained as special cases, including various forms of the Efficient Market Hypoth...

Return Predictability under Knightian Uncertainty

The predictability of stock and bond excess returns is investigated from an investment perspective in the presence of Knightian uncertainty. Uncertainty about the return distribution is formalized with the maxmin expected utility approach of Gilboa and Schmeidler (1989). It is analyzed how risk and uncertainty aversion di¤er in their e¤ects on optimal portfolio choice. Most importantly, it is s...

Planning under Risk and Knightian Uncertainty

Two noteworthy models of planning in AI are probabilistic planning (based on MDPs and its generalizations) and nondeterministic planning (mainly based on model checking). In this paper we: (1) show that probabilistic and nondeterministic planning are extremes of a rich continuum of problems that deal simultaneously with risk and (Knightian) uncertainty; (2) obtain a unifying model for these pro...

Regulating Nonlinear Environmental Systems under Knightian Uncertainty

Consumption and Saving Under Knightian Uncertainty

This paper studies consumption/saving problem under Knightian uncertainty in a two period setting. The multiple-priors utility model is adopted. The effects of income uncertainty and capital uncertainty on optimal savings are analyzed by deriving closed form solutions.