16,121 research outputs found
Clark-Ocone type formula for non-semimartingales with finite quadratic variation
We provide a suitable framework for the concept of finite quadratic variation
for processes with values in a separable Banach space using the language of
stochastic calculus via regularizations, introduced in the case by the
second author and P. Vallois. To a real continuous process we associate the
Banach valued process , called {\it window} process, which describes
the evolution of taking into account a memory . The natural state
space for is the Banach space of continuous functions on
. If is a real finite quadratic variation process, an
appropriated It\^o formula is presented, from which we derive a generalized
Clark-Ocone formula for non-semimartingales having the same quadratic variation
as Brownian motion. The representation is based on solutions of an infinite
dimensional PDE
Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations
The paper reminds the basic ideas of stochastic calculus via regularizations
in Banach spaces and its applications to the study of strict solutions of
Kolmogorov path dependent equations associated with "windows" of diffusion
processes. One makes the link between the Banach space approach and the so
called functional stochastic calculus. When no strict solutions are available
one describes the notion of strong-viscosity solution which alternative (in
infinite dimension) to the classical notion of viscosity solution.Comment: arXiv admin note: text overlap with arXiv:1401.503
On stochastic calculus related to financial assets without semimartingales
This paper does not suppose a priori that the evolution of the price of a
financial asset is a semimartingale. Since possible strategies of investors are
self-financing, previous prices are forced to be finite quadratic variation
processes. The non-arbitrage property is not excluded if the class
of admissible strategies is restricted. The classical notion of
martingale is replaced with the notion of -martingale. A calculus
related to -martingales with some examples is developed. Some
applications to no-arbitrage, viability, hedging and the maximization of the
utility of an insider are expanded. We finally revisit some no arbitrage
conditions of Bender-Sottinen-Valkeila type
Knowledge-Intensive Processes: Characteristics, Requirements and Analysis of Contemporary Approaches
Engineering of knowledge-intensive processes (KiPs) is far from being mastered, since they are genuinely knowledge- and data-centric, and require substantial flexibility, at both design- and run-time. In this work, starting from a scientific literature analysis in the area of KiPs and from three real-world domains and application scenarios, we provide a precise characterization of KiPs. Furthermore, we devise some general requirements related to KiPs management and execution. Such requirements contribute to the definition of an evaluation framework to assess current system support for KiPs. To this end, we present a critical analysis on a number of existing process-oriented approaches by discussing their efficacy against the requirements
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