Martingale measures and hedging for discrete-time financial markets

• 成果类型: Article
• 署名作者: Schäl, M
• 署名单位: University of Bonn
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.24.2.509
• 发表日期: 1999
• 页码: 509-528
• 关键词: CONTINGENT CLAIMS; THEOREM

摘要

The price of stocks is modelled by a discrete-time, square-integrable, vector-valued process X. No further boundedness condition on X is imposed. Contingent claims X are described by square-integrable random variables. One looks for values nu of the initial wealth nu that allow for super-hedging H by some portfolio plan. In several cases, the smallest value nu is known to coincide with the maximal expectation of H under equivalent martingale measures. Here, within an L-2-framework, another sufficient condition is provided which can be looked upon as a stronger form of the no-arbitrage condition. The mathematical tool and one of the main contributions is an optional decomposition theorem for a process which is a supermartingale under any equivalent martingale measure. The upper price process for a contingent claim is shown to be a typical example for such a process. Moreover it is shown that in a Markovian model one can restrict attention to Markovian portfolio plans and to Markovian martingale measures.