A General Benchmark Model for Stochastic Jump Sizes

This paper extends the benchmark framework of Platen (2002) and Platen (2004b). It introduces a sequence of incomplete markets, having uncertainty driven by an m-dimensional 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. It also provides a clear link to fundamental variables of the market, the market prices of risk. The connection between traded securities, arbitrage and market incompleteness is analyzed. This paper aims to provide a framework for analyzing the degree of incompleteness associated with jump processes, a problem well-known from insurance and credit risk modeling. Furthermore, by staying under the empirical measure, the resulting benchmark model has potential advantages for various applications in finance and insurance.