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A class of complete benchmark models with intensity-based jumps

Part of: Applications Mathematical economics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Eckhard Platen
Eckhard Platen*
Affiliation:
University of Technology, Sydney
*
∗ Postal address: School of Finance and Economics and Department of Mathematical Sciences, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia. Email address: [email protected]
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Abstract

This paper proposes a class of complete financial market models, the benchmark models, with security price processes that exhibit intensity-based jumps. The benchmark or reference unit is chosen to be the growth-optimal portfolio. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. In the proposed framework an equivalent risk-neutral measure need not exist. Benchmarked fair derivative prices are obtained as conditional expectations of future benchmarked prices under the real-world probability measure. This concept of fair pricing generalizes the classical risk-neutral approach and the actuarial present-value pricing methodology.

Keywords

Benchmark modeljump diffusionsgrowth-optimal portfolioevent risk premiumfair pricingactuarial pricinginsurance

MSC classification

Primary: 91B24: Price theory and market structure
Secondary: 60G30: Continuity and singularity of induced measures 62P20: Applications to economics
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 19 - 34
Copyright
Copyright © Applied Probability Trust 2004 

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