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Minimal martingale measures for jump diffusion processes

Part of: Markov processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Takuji Arai
Takuji Arai*
Affiliation:
Tokyo University of Science
*
∗ Postal address: Department of Information Sciences, Tokyo University of Science, Noda, Chiba, 278-8510, Japan. Email address: arai@is.noda.tus.ac.jp
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Abstract

We consider an incomplete market model whose stock price fluctuation is given by a jump diffusion process. For this model, we calculate the density process of the minimal martingale measure. Also, we state the relation to a locally risk-minimizing strategy.

Keywords

Minimal martingale measureincomplete marketjump diffusion processlocally risk minimizing

MSC classification

Primary: 60J75: Jump processes
Secondary: 91B70: Stochastic models
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 263 - 270
Copyright
Copyright © Applied Probability Trust 2004 

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References

Chan, T. (1999). Pricing contingent claims on stocks driven by Lévy processes. Ann. Appl. Prob. 9, 504–528.CrossRefGoogle Scholar
Choulli, T., Krawczyk, L., and Stricker, C. (1998). E-martingales and their applications in mathematical finance. Ann. Prob. 26, 853–876.Google Scholar
Föllmer, H., and Schweizer, M. (1991). Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis (Stoch. Monogr. 5), eds Davis, M. H. A. and Elliott, R. J., Gordon and Breach, New York, pp. 389–414.Google Scholar
Föllmer, H., and Sondermann, D. (1986). Hedging of nonredundant contingent claims. In Contributions to Mathematical Economics, eds Hildenbrand, W. and Mas-Colell, A., North-Holland, Amsterdam, pp. 205–223.Google Scholar
Pham, H. (2000). On quadratic hedging in continuous time. Math. Meth. Operat. Res. 51, 315–339.Google Scholar
Protter, P. (1990). Stochastic Integration and Differential Equations. A New Approach. Springer, Berlin.Google Scholar
Schweizer, M. (1991). Option hedging for semimartingales. Stoch. Process. Appl. 37, 339–363.Google Scholar
Schweizer, M. (2001). A guided tour through quadratic hedging approaches. In Option Pricing, Interest Rates and Risk Management, eds Jouini, E., Cvitanić, J. and Musiela, M., Cambridge University Press, pp. 538–574.CrossRefGoogle Scholar