Asset price bubbles under model uncertainty and short-sale constraints: A discrete-time analysis

Wenqing Zhang and Lin Zhang

Papers from arXiv.org

Abstract: In this study, we investigate asset price bubbles in a discrete-time, discrete-state market under model uncertainty and short-sale constraints. Using a super-hedging valuation benchmark, we study the difference between the asset's market price and its fundamental value in this constrained market. We examine how assumptions on the liquidation time affect the conditional expectation bounds satisfied by the resulting bubble process. For assets with bounded maturity and no dividend payments, the G-supermartingale property of prices provides a necessary and sufficient condition for the existence of bubbles. In contrast, when maturity is unbounded, the infi-supermartingale property yields a necessary condition, while the G-supermartingale property remains sufficient. We also show that no dominance rules out bubbles when the liquidation time is bounded. For finite-horizon contingent claims, we distinguish upper-valuation relations from no-dominance benchmarks. Fundamental prices satisfy put-call bounds, whereas market prices satisfy put-call parity under no dominance. In the dividend-free setting, the same assumptions imply equality between American and European call fundamental values and, under the stated trading conditions, between their market prices.

Date: 2025-12, Revised 2026-09
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