This paper introduces the notion of an {Ft, 0 ≤ t ≤ T}-consistent dynamic operator with a floor, by suitably formulating four axioms. It is shown that an {Ft, 0 ≤ t ≤ T}consistent dynamic operator {Es,t, 0 ≤ s ≤ t ≤ T} with a continuous upper-bounded floor S is necessarily represented by the solution of a backward stochastic differential equation (BSDE) reflected upwards on the floor, if it is ...

The representation of linear operators, on the Banach space of Bochner integrable functions, has been the object of much study for the past fifty years. Dunford and Pettis began this investigation in 1940 with the representation of weakly compact and norm compact operators on L1(R) by a Bochner integral, see [6,8]. Andrews has extended their study to the case of the space L1(E), of E-valued, Bo...

We present a purely group-theoretical derivation of the continuous wavelet transform (CWT) on the (n ? 1)-sphere S n?1 , based on the construction of general coherent states associated to square integrable group representations. The parameter space of the CWT, Y SO(n)R + , is embedded into the generalized Lorentz group SO o (n; 1) via the Iwasawa decomposition, so that X ' SO o (n; 1)=N, where ...

This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. This feature occurs since, contrary ...

We study regression models for the situation where both dependent and independent variables are square integrable stochastic processes. Questions concerning definition and existence of the corresponding functional linear regression models and some basic properties are explored. We derive a representation of the regression parameter function in terms of the canonical components of the processes ...

We develop a non-anticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by B Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative ad...