On the Second Fundamental Theorem of Asset Pricing

2015/12/12 by Rajeeva L Karandikar, Rajeeva L. Karandikar, B. V. Rao +3
Economics, Econometrics and Finance · Mathematics · #60G44 #62P05 #91G20 #97M30 #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G44 #msc:62P05 #msc:91G20 #msc:97M30

paper · pdf · doi:10.48550/arxiv.1512.03881

arxiv created 2015/12/12 · openalex publication_date 2015/12/12 · arxiv updated 2015/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X¹,…, X^d be sigma-martingales on (Ω,\cal F, P). We show that every bounded martingale (with respect to the underlying filtration) admits an integral representation w.r.t. X¹,…, X^d if and only if there is no equivalent probability measure (other than P) under which X¹,…,X^d are sigma-martingales. From this we deduce the second fundamental theorem of asset pricing- that completeness of a market is equivalent to uniqueness of Equivalent Sigma-Martingale Measure (ESMM).

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