DENSITY OF THE SET OF PROBABILITY MEASURES WITH THE MARTINGALE REPRESENTATION PROPERTY

• 成果类型: Article
• 署名作者: Kramkov, Dmitry; Pulido, Sergio
• 署名单位: Carnegie Mellon University; Universite Paris Saclay; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1321
• 发表日期: 2019
• 页码: 2563-2581
• 关键词: endogenous completeness; continuous-time; equilibrium

摘要

Let psi be a multidimensional random variable. We show that the set of probability measures Q such that the Q-martingale S-t(Q) = E-Q[psi vertical bar F-t] has the Martingale Representation Property (MRP) is either empty or dense in L-infinity-norm. The proof is based on a related result involving analytic fields of terminal conditions (psi (x))(x)(is an element of U) and probability measures (Q(x))(x)(is an element of U) over an open set U. Namely, we show that the set of points x is an element of U such that S-t(x) = E-Q(x)[psi (x)vertical bar F-t] does not have the MRP, either coincides with U or has Lebesgue measure zero. Our study is motivated by the problem of endogenous completeness in financial economics.