On the pricing of American contingent claims under transaction costs and multiple risky assets |
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| Institution: | 1. Department of Mathematics, Huzhou University, Huzhou 313000, China;2. College of Science, Wenzhou Medical College, Wenzhou 325035, China;1. School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, PR China;2. School of Environmental and Biological Science and Technology, Dalian University of Technology, Dalian, Liaoning 116012, PR China;3. School of Energy and Engineering, Dalian University of Technology, Dalian, Liaoning 116024, PR China;1. School of Computer Science and Technology, Dalian University of Technology, Dalian, China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China;3. Department of Computer Science, Dalian Neusoft Institute of Technology, Dalian, China;1. College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics, NWNU & IMP CAS, Northwest Normal University, and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China;2. State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China;3. Department of Physics, Lanzhou University, Lanzhou 730000, China;1. College of Mechanical and Electronic Engineering, China University of Geosciences, Wuhan 430074, China;2. Department of Mechanics, Tianjin University, Tianjin 300072, China;3. School of Engineering, University of California, Merced, CA 95343, USA |
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| Abstract: | This paper addresses the hedging problem of American Contingents Claims (ACCs) in the framework of continuous-time Itô models for financial market. The special feature of this paper is that in the financial market the investor has to face fixed and proportional transaction costs when trading multiple risky assets. By using the auxiliary martingale approach and extending the results of Cvitanic and Karatzas Cvitanic J, Karatzas I. Hedging and portfolio optimization under transaction costs: a martingale approach. Math Finance 1996;6:135–65] on pricing European contingent with transaction costs in the single-stock market, an arbitrage-free interval hlow, hup] is identified, and the end points are characterized by auxiliary martingales and stopping times in terms of auxiliary stochastic control problems. Here hup and hlow are so-called the upper hedging price and the lower hedging price. |
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