We consider the maximization of the long-term growth rate in the Black–Scholes model under proportional transaction costs as in Taksar et al. (Math. Oper. Res. 13:277–294, <CitationRef CitationID="CR24">1988</CitationRef>). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341–1358, <CitationRef CitationID="CR14">2010</CitationRef>) for optimal consumption over...</citationref></citationref>

We present a unified approach to Doob's $L^p$ maximal inequalities for $1\leq p\infty$. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging....

An instalment option is a European option in which the premium, instead of being paid up-front, is paid in a series of instalments. If all instalments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option...

Let ("S_t")_"t&epsi;I" be an R-super-d-valued adapted stochastic process on (Ω, , (_"t")_"t&epsi;I", "P"). A basic problem occurring notably in the analysis of securities markets, is to decide whether there is a probability measure "Q" on  equivalent to "P" such that ("S_t")_"t&epsi;I" is a martingale with...

We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial...

We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law-invariant monetary utility functions or equivalently, law-invariant risk measures. We first prove existence of an optimal risk sharing allocation which is in addition...