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.

An installment option is a European option in which the premium, instead of being paid up-front, is paid in a series of installments. If all installments 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...

In securities markets, the characterization of the absence of arbitrage by the existence of state price deflators is generally obtained through the use of the Kreps-Yan theorem.This paper deals with the validity of this theorem (see Kreps, 1981, and Yan, 1980) in a general framework. More...

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...

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 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>