Every submartingale S of class D has a unique Doob–Meyer decomposition S=M+A, where M is a martingale and A is a predictable increasing process starting at 0.

In this paper we investigate model-independent bounds for exotic options written on a risky asset using infinite-dimensional linear programming methods. Based on arguments from the theory of Monge–Kantorovich mass transport, we establish a dual version of the problem that has a natural...

Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff . Economic intuition suggests that high risk aversion leads to a rather concentrated...

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 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>

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...