Optimal strategies and utility-based prices converge when agents' preferences do

• 成果类型: Article
• 署名作者: Carassus, Laurence; Rasonyi, Miklos
• 署名单位: Universite Paris Cite; Hungarian Academy of Sciences; HUN-REN; HUN-REN Institute for Computer Science & Control
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1060.0220
• 发表日期: 2007
• 页码: 102-117
• 关键词: fundamental theorem; martingale measures; incomplete markets; Optimal investment; arbitrage

摘要

A discrete-time financial market model is considered with a sequence of investors whose preferences are described by their utility functions U-n, defined on the whole real line and assumed to be strictly concave and increasing. Under suitable hypotheses, it is shown that whenever U-n tends to another utility function U-infinity the respective optimal strategies converge, too. Under additional assumptions the rate of convergence is estimated. We also establish the continuity of the fair price of Davis [Davis, M. H. A. 1997. Option pricing in incomplete markets. M. A. H. Dempster, S. R. Pliska, eds. Mathematics of Derivative Securities. Cambridge University Press, pp. 216-226] and the utility indifference price of Hodges and Neuberger [Hodges, R., K. Neuberger. 1989. Optimal replication of contingent claims under transaction costs.