Information, no-arbitrage and completeness for asset price models with a change point

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Fontana, Claudio¹  Grbac, Zorana²  Jeanblanc, Monique¹  Li, Qinghua³ 

[1] Univ Evry Val Essonne, Lab Math & Modelisat, F-91037 Evry, France

[2] Univ Paris Diderot, Lab Probabil & Modeles Aleatoires, F-75205 Paris 13, France

[3] Humboldt Univ, Inst Math, D-10099 Berlin, Germany

关键词: Enlargement of filtration;    Martingale representation;    Random time;    Change point;    Regime switching;    Arbitrage of the first kind;    Free lunch with vanishing risk;   

DOI  :  10.1016/j.spa.2014.04.010

来源: Elsevier

【 摘 要 】

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time tau. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in all the filtrations which naturally arise in this setting, establishing martingale representation results and characterizing the validity of the NA1 and NFLVR no-arbitrage conditions. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free