Filipovic, DamirTappe, StefanTeichmann, Josef2013-08-122013-08-122013-08-12201010.1137/090758593https://infoscience.epfl.ch/handle/20.500.14299/940550905.1413In the spirit of Bjork-DiMasi-Kabanov-Runggaldier, we investigate term structure models driven by Wiener process and Poisson measures with forward curve dependent volatilities. This includes a full existence and uniqueness proof for the corresponding Heath--Jarrow--Morton type term structure equation. Furthermore, we characterize positivity preserving models by means of the characteristic coefficients, which was open for jump-diffusions. Additionally we treat existence, uniqueness and positivity of the Brody-Hughston equation of interest rate theory with jumps, an equation which we believe to be very useful for applications. A key role in our investigation is played by the method of the moving frame, which allows to transform the Heath--Jarrow--Morton--Musiela equation to a time-dependent SDE.term structure models driven by Wiener processes and Poisson measuresHeath-Jarrow-Morton-Musiela equationPositivity preserving modelstext::journal::journal article::research article