Related papers: Independence and indifferent points imply continui…
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…
The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model, and provides two linear approximations for the utility indifference price. The key tool is a probabilistic representation for the…
We introduce a new interpretation of two related notions - conditional utility and utility independence. Unlike the traditional interpretation, the new interpretation renders the notions the direct analogues of their probabilistic…
In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one…
Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic…
We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
We introduce a new kind of free independence, called real infinitesimal freeness. We show that independent orthogonally invariant with infinitesimal laws are asymptotically real infinitesimally free. We introduce new cumulants, called real…
We introduce finite support iterations of symmetric systems, and use them to provide a strongly modernized proof of David Pincus' classical result that the axiom of dependent choice is independent over ZF with the ordering principle…
In this paper we introduce the inaccessible game, an information-theoretic dynamical system constructed from four axioms. The first three axioms are known and define \emph{information loss} in the system. The fourth is a novel…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
A compositional Petri net-based semantics is given to a simple language allowing pointer manipulation and parallelism. The model is then applied to give a notion of validity to the judgements made by concurrent separation logic that…
We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents' substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the…
We define an invariant of triple-point-free immersions of $2$-spheres into Euclidean $3$-space, taking values in $l^1(\mathbb{Z})$. It remains unchanged under regular homotopies through such immersions. An explicit description of its image…
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras…
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…
To explain conceptual gap between classical/quantum and other, hypothetical descriptions of world, several principles has been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce…
In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the…