Economics-Based Financial Bubbles (and Why They Imply Strict Local Martingales)

Abstract

We introduce a new and numéraire-independent approach for defining and analysing financial bubbles in general, incomplete markets. We define our concepts in an economically motivated way using only primal quantities like assets and trading strategies. We then derive dual characterisations involving numéraires and martingale measures and show that a market is (interesting) bubbly in our sense if and only if all possible valuation measures for all possible discounted asset prices always lead to strict local martingales. In contrast to other approaches for bubble definitions in incomplete markets, our notion of a bubble is robust in the sense that it does not depend on the choice of a particular risk-neutral measure. We illustrate our results and concepts by many explicit and concrete examples; these include an incomplete market which is (interesting) bubbly, an incomplete market where one valuation measure sees a bubble while a second does not, and a natural setup where bubble birth occurs endogenously.