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Existence and stability of measure solutions for BSDE with generators of quadratic growth

Please always quote using this URN:urn:nbn:de:0296-matheon-8293
  • With an emphasis on generators with quadratic growth in the control variable we consider measure solutions of BSDE, a solution concept corresponding to the notion of risk neutral measure in mathematical finance. In terms of measure solutions, solving a BSDE reduces to martingale representation with respect to an underlying filtration. Measure solutions related to measures equivalent to the historical one provide classical solutions. We derive the existence of measure solutions in scenarios in which the generating functions are just continuous, of at most linear growth in the control variable (corresponding to generators of at most quadratic growth in the usual sense), and with a random bound in the time parameter whose stochastic integral is a BMO martingale. Our main tools include a stability property of sequences of measure solutions, for which a limiting solution is obtained by means of the weak convergence of measures.

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Metadaten
Author:Alexander Fromm, Peter Imkeller, Jianing Zhang
URN:urn:nbn:de:0296-matheon-8293
Referee:Dirk Becherer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/01/27
Release Date:2012/01/27
Tag:
Institute:Humboldt-Universität zu Berlin
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
Preprint Number:883
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