TY - GEN A1 - Ankirchner, Stefan A1 - Imkeller, Peter A1 - Popier, Alexandre T1 - On measure solutions of backward stochastic differential equations N2 - We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the generator is seen as vanishing, so that the classical solution can be reconstructed by a combination of the operations of conditioning and using martingale representations. In case the terminal condition ist bounded and the generator fulfills the usual continuity and boundedness conditions, we show the measure solutions with equivalent measures just reinterpret classical ones. In case of terminal conditions that have only exponentially bounded moments, we discuss a series of examples which show that in cas of non-uniqueness classical solutions that fail to be measure solutions can coexists with different measure solution. KW - backward stochastic differential equation KW - stochastic control KW - hedging of contingent claim KW - martingale measure KW - martingale representation KW - Girsanov's theorem KW - weak solution KW - measure solution KW - Brownian motion Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/636 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6369 ER -