Local risk minimization and numéraire

Biagini, F. and Pratelli, M. (1999): Local risk minimization and numéraire. In: Journal of Applied Probability, Vol. 36, No. 4: pp. 1126-1139

Abstract

The ‘change of numéraire’ technique has been introduced by Geman, El Karoui and Rochet for pricing and hedging contingent claims in the case of complete markets. In this paper we study the ‘change of numéraire’ using the ‘locally risk-minimizing approach’, when the market is not complete. We prove that, if the stochastic process which represents the prices is continuous, the l.r.m. strategy is invariant by a change of numéraire (this result is false in the right-continuous case, as is shown by some counterexamples).

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0021-9002
• Language: English