SFB 303 Discussion Paper No. B - 424

Author: Wiesenberg, Holger
Title: Modeling Market Risk in a Jump-Diffusion Setting: A Generalized Hofmann-Platen-Schweizer-Model
Abstract: We generalize the paper of Hofmann, Platen and Schweizer [HPS92] to jump-diffusion models. First we introduce securities which are replicable in a self-financing way. Then we characterize market risks which are in a special way 'orthogonal' to these securities. Moreover we prove, that every general arbitrage-free security has a unique decomposition into a self-financing replicable security and such a market risk.
Then we discuss the martingale measures for our jump-diffusion model. In particular we examine the minimal equivalent martingale measure and show that in our model the minimal martingale measure preserves is charcterized in preserving the market risk processes under a change of measure. But we state also that unlike the continuous case it does not preserve the orthogonality to the martingale part of the underlyings.
Keywords: jump-diffusion models, minimal martingale measure, orthogonality, self-financing strategies and portfolios, arbitrage-free securities, self-financing replicable securities, unhedgable market risks
JEL-Classification-Number: G13
Creation-Date: 15.03.1998
URL: ../1998/b/bonnsfb424.pdf

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