Asset Price Bubbles

Robert A. Jarrow
2015 Annual Review of Financial Economics  
This article reviews the theoretical literature on asset price bubbles, with an emphasis on the martingale theory of bubbles. The key questions studied are as follows: First, under what conditions can asset price bubbles exist in an economy? Second, if bubbles exist, what are the implications for the pricing of derivatives on the bubble-laden asset? Third, if bubbles can exist, how can they be empirically determined? Answers are provided for three frictionless and competitive economies with
more » ... easingly restrictive structures. The least restrictive economy just assumes no arbitrage. The next satisfies no arbitrage and no dominance. The third assumes the existence of an equilibrium. We consider a continuous or discrete time model on the time interval [0, T ], where T can be a fixed finite time or ∞. For simplicity, we give the notation for a continuous time model and discuss the discrete time model's differences via remarks. Let ( , F, F, P) be a filtered complete probability space characterizing the randomness in the economy. We assume that the filtration F = (F t ) t≥0 satisfies the usual hypotheses (Protter 2001) . Markets are competitive and frictionless. Competitive means that traders act as price takers, believing their trades have no quantity impact on market price. Frictionless means that there are no transaction costs and no trading constraints, e.g., short sale constraints or margin requirements, and that shares are not infinitely divisible. 202 Jarrow Annu. Rev. Financ. Econ. 2015.7:201-218. Downloaded from www.annualreviews.org Access provided by 207.241.225.227 on 05/07/20. For personal use only. 1 A stochastic process X is a semimartingale if it has a decomposition X t = X 0 + M t + A t , where (a) M 0 = A 0 = 0; (b) A is adapted, càdlàg, and of finite variation on compacts; and (c) M is a local martingale (hence càdlàg) (Protter 2001, chapter 2).
doi:10.1146/annurev-financial-030215-035912 fatcat:dakc3cksl5ec7jfsx2lcxqelci