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2019•Unpublished venueRequires access

The Esscher Transform and the Minimal Martingale Measure

Tomas Björk

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Abstract

Abstract In this chapter we present two ways to choose a unique martingale measure in an incomplete market. The first way is to use an extended version of the Esscher transform, which implies that we restrict the class of martingale measures. The second way is to use the minimal martingale measure, that is, the measure which minimizes the norm of the associated Girsanov kernel. We exemplify the two methods and discuss the economic significance.

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What this paper is about

Abstract In this chapter we present two ways to choose a unique martingale measure in an incomplete market. The first way is to use an extended version of the Esscher transform, which implies that we restrict the class of martingale measures. The second way is to use the minimal martingale measure, that is, the measure which minimizes the norm of the associated Girsanov kernel. We exemplify the two methods and discuss the economic significance.

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Available abstract

Abstract In this chapter we present two ways to choose a unique martingale measure in an incomplete market. The first way is to use an extended version of the Esscher transform, which implies that we restrict the class of martingale measures. The second way is to use the minimal martingale measure, that is, the measure which minimizes the norm of the associated Girsanov kernel. We exemplify the two methods and discuss the economic significance.

Key concepts: Martingale pricing, Martingale (probability theory), Measure (data warehouse), Mathematics, Local martingale, Economics, Econometrics, Applied mathematics

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