146 research outputs found
On a dyadic approximation of predictable processes of finite variation
We show that any cadlag predictable process of finite variation is an a.s.
limit of elementary predictable processes; it follows that predictable stopping
times can be approximated `from below' by predictable stopping times which take
finitely many values. We then obtain as corollaries two classical theorems:
predictable stopping times are announceable, and an increasing process is
predictable iff it is natural.Comment: version 5: To make the paper more readable I made the paper more self
contained, and I have changed the order with which theorems are stated and
prove
Optimal investment and price dependence in a semi-static market
This paper studies the problem of maximizing expected utility from terminal
wealth in a semi-static market composed of derivative securities, which we
assume can be traded only at time zero, and of stocks, which can be traded
continuously in time and are modeled as locally-bounded semi-martingales.
Using a general utility function defined on the positive real line, we first
study existence and uniqueness of the solution, and then we consider the
dependence of the outputs of the utility maximization problem on the price of
the derivatives, investigating not only stability but also differentiability,
monotonicity, convexity and limiting properties.Comment: 31 pages. I have decided to merge the paper arXiv:1210.5466 with the
version 1 of the present paper. This version 2 is the result of the merg
Pathwise Stochastic Calculus with Local Times
We study a notion of local time for a continuous path, defined as a limit of
suitable discrete quantities along a general sequence of partitions of the time
interval. Our approach subsumes other existing definitions and agrees with the
usual (stochastic) local times a.s. for paths of a continuous semimartingale.
We establish pathwise version of the It\^o-Tanaka, change of variables and
change of time formulae. We provide equivalent conditions for existence of
pathwise local time. Finally, we study in detail how the limiting objects, the
quadratic variation and the local time, depend on the choice of partitions. In
particular, we show that an arbitrary given non-decreasing process can be
achieved a.s. by the pathwise quadratic variation of a standard Brownian motion
for a suitable sequence of (random) partitions; however, such degenerate
behavior is excluded when the partitions are constructed from stopping times.Comment: minor change
Do arbitrage-free prices come from utility maximization?
In this paper we ask whether, given a stock market and an illiquid
derivative, there exists arbitrage-free prices at which an utility-maximizing
agent would always want to buy the derivative, irrespectively of his own
initial endowment of derivatives and cash. We prove that this is false for any
given investor if one considers all initial endowments with finite utility, and
that it can instead be true if one restricts to the endowments in the interior.
We show however how the endowments on the boundary can give rise to very odd
phenomena; for example, an investor with such an endowment would choose not to
trade in the derivative even at prices arbitrarily close to some arbitrage
price.Comment: this version: streamlined the paper, fixed typos, cut discussions
when introducing the model, deleted Section 9 and part of Section 8, changed
bib styl
Towards an Interaction-based Integration of MKM Services into End-User Applications
The Semantic Alliance (SAlly) Framework, first presented at MKM 2012, allows
integration of Mathematical Knowledge Management services into typical
applications and end-user workflows. From an architecture allowing invasion of
spreadsheet programs, it grew into a middle-ware connecting spreadsheet, CAD,
text and image processing environments with MKM services. The architecture
presented in the original paper proved to be quite resilient as it is still
used today with only minor changes.
This paper explores extensibility challenges we have encountered in the
process of developing new services and maintaining the plugins invading
end-user applications. After an analysis of the underlying problems, I present
an augmented version of the SAlly architecture that addresses these issues and
opens new opportunities for document type agnostic MKM services.Comment: 14 pages, 7 figure
Comparing Techniques for Mobile Interaction with Objects from the Real World.
Mobile interaction with objects from the real world is gaining in popularity and importance as different mobile technologies increasingly provide the basis for the extraction and usage of information from physical objects. So far, Physical Mobile Interaction is used in rather simple ways. This paper presents a comparison and evaluation of more complex and sophisticated techniques for Physical Mobile Interaction. The results indicate the importance of usability guidelines that pay attention to these new interaction techniques
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