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A General Benchmark Model for Stochastic Jump Sizes

Morten Christensen and Eckhard Platen ()

No 139, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper extends the benchmark framework of Platen (2002) by introducing a sequence of incomplete markets, having uncertainty driven by a Wiener process and a marked point process. By introducing an idealized market, in which all relevant economical variables are observed, but may not all be traded, a generalized growth optimal portfolio (GOP) is obtained and calculated explicitly. The problem of determining the GOP is solved in a general setting which extends existing treatments and provides a clear link to the market prices of risk. The connection between traded securities, arbitrage and market incompleteness is analyzed. This provides a framework for analyzing the degree of incompleteness associated with jump processes, a problem well-known from insurance and credit risk modeling. By staying under the empirical measure, the resulting benchmark model has potential advantages for various applications in finance and insurance.

Pages: 27 pages
Date: 2004-11-01
New Economics Papers: this item is included in nep-fmk and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Published as: Christensen, C. and Platen, E., 2005, "A General Benchmark Model for Stochastic Jump Sizes", Stochastic Analysis and Applications, 23(5), 1017-1044.

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