For small involutive and integral quantaloids Q it is shown that covariant presheaves on symmetric Q-categories are equivalent to certain subalgebras of a speci c monad on the category of symmetric Q-categories. This construction is related to a weakening of the subobject classi er axiom which does not require the classi cation of all subalgebras, but only guarantees that classi able subalgebra...

By means of classical Itô’s calculus we decompose option prices as the sum of the classical Black-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due by correlation and a term due to the volatility of the volatility. This decomposition allows us to develop …rst and second-order approximation formulas for option prices and implied vol...

BDDs provide an established technique for propositional formula manipulation. In this paper we re-develop the basic BDD theory using standard rewriting techniques. Since a BDD is a DAG instead of a tree we need a notion of shared rewriting and develop appropriate theory. A rewriting system is presented by which canonical ROBDDs can be obtained. For this rewriting system a layerwise strategy is ...

The problem of scheduling jobs that arrive over time on a single machine is well-studied. We study the preemptive model and the model with restarts. We provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and unweighted total ow time. By using new techniques, we provide the rst lower bounds ...

This paper proposes an integrated approach to discrete time modelling in nance and insurance This approach is based on the existence of a speci c benchmark portfolio known as the growth optimal portfolio When used as numeraire this portfolio ensures that all benchmarked price processes are supermartingales A fair price is characterized in terms of the type of maximum that the growth rate of the...

We de ne a value-based modal -calculus, built from rst-order formulas, modalities, and xed point operators parameterized by data variables, which allows to express temporal properties involving data. We interpret this logic over CRL terms de ned by linear process equations. The satisfaction of a temporal formula by a CRL term is translated to the satisfaction of a rst-order formula containing p...

Schnyder characterized planar graphs in terms of order dimension. This seminal result found several extensions. A particularly far reaching extension is the Brightwell-Trotter Theorem about planar maps. It states that the order dimension of the incidence poset PM of vertices, edges and faces of a planar map M has dimension at most 4. The original proof generalizes the machinery of Schnyder-path...

In this paper we prove two new results about closed semigroups in the family of solvable groups Hmn := R nφ R where φ, the structure homomorphism, maps nontrivially into the center of Aut(Rn). The rst result states that the closure of a semigroup generated by a set in Hmn that is not included in a maximal semigroup with nonempty interior is actually a group. The second result states that among ...

The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues's Theorem, harmonic conjugates, projectivities, involutions, conics, Pascal's Theorem, poles and polars. The axioms used for the synthetic treatment are constructive versions of the traditional axioms. The analytic construction is used to verify t...

For xed c, Prolate Spheroidal Wave Functions (PSWFs), denoted by ψn,c, form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith c. They have been largely studied and used after the seminal work of D. Slepian and his co-authors. In several applications, uniform estimates of the ψn,c in n and c, are needed. To progress in this direction, we push fo...