A semimartingale BSDE related to the minimal entropy martingale measure
type: Item
instance of: scholarly article
title: A semimartingale BSDE related to the minimal entropy martingale measure
zbMATH Open document ID: 1063.91037
author: M. Mania
author: Marina Santacroce
author: R. Tevzadze
published in: Finance and Stochastics
publication date: 2005-05-20T00:00:00Z
review text: In complete markets every contingent claim is replicable and the price of the claim is determined using the uniquely defined martingale measure. If the market is incomplete the set of martingale measures is not in general a singleton and there is an interval of arbitrage-free prices associated to different pricing martingale measures. The choice of the pricing measure is not longer preference-tree and depends on the utility functions of the investors or on the criterion relative to which the hedging error is measured. The most popular choices of pricing measures are the minimal martingale measure introduced by \textit{H. Föllmer} and \textit{M. Schweizer} [Applied stochastic analysis, Pap. Workshop, London/UK 1989, Stochastic Monogr. 5, 389-414 (1990; Zbl 0738.90007)] and the variance-optimal martingale measure (see \textit{F. Delbaen} and \textit{W. Schachermayer} [Bernoulli 2, No. 1, 81-105 (1996; Zbl 0849.60042)], \textit{M. Schweizer} [Ann. Probab. 24, No. 1, 206-236 (1996; Zbl 0854.60045)]). The variance-optimal martingale measure is determined by minimizing the \(L_2\)-norm of densities of the martingale measure with respect to the basic measure \(P\) among all signed martingale measures and represents the best choice when the quality of the hedging strategies is measured by the quadratic criterion. An another possibility is the minimal entropy martingale measure which minimizes the relative entropy of a martingale measure with respect to the measure \(P\) and is known to be closely related to the exponential hedging problem. For a locally bounded process \(X\) the minimal entropy martingale measure exists, is unique and if there is a martingale measure with the finite relative entropy, then the minimal entropy martingale measure is equivalent to \(P\). Using the dynamic programming technique the authors of this paper propose a construction of the minimal entropy martingale measure in the case where the dynamics of the discounted assets price is described by a…
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 90C39
zbMATH DE Number: 2169535
zbMATH Keywords: semimartingale backward equation
zbMATH Keywords: contingent claim pricing
zbMATH Keywords: incomplete markets
reviewed by: M. P. Moklyachuk
MaRDI profile type: Publication
full work available at URL: s007800200090
OpenAlex ID: W2049837257
DOI: 10.1007/S007800200090
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description: scientific article; zbMATH DE number 2169535