We study the detailed convergence of the binomial tree scheme. It is known that the scheme is first order. We find the exact constants, and show it is possible to modify Richardson extrapolation to get a method of order three-halves. We see that the delta, used in hedging, converges at the same rate. We analyze this by first embedding the tree scheme in the Black-Scholes diffusion model by mean...

An edge-colored graph G is conflict-free connected if, between each pair of distinct vertices, there exists a path containing a color used on exactly one of its edges. The conflict-free connection number of a connected graph G, denoted by cfc(G), is defined as the smallest number of colors that are required in order to make G conflict-free connected. A coloring of vertices of a hypergraph H = (...

Developed only recently, support vector learning machines achieve high generalization ability by minimizing a bound on the expected test error; however, so far there existed no way of adding knowledge about invariances of a classiication problem at hand. We present a method of incorporating prior knowledge about transformation invari-ances by applying transformations to support vectors, the tra...

In this paper we propose a Symmetrical Binomial Lattice Approach that is equivalent to the well‐known and widely utilized Lattice of Cox, Ross & Rubinstein (1979) when modeling Geometric Brownian Motion type of processes, but can be utilized for a wide variety of other Markov style stochastic processes. This is due to the highly intuitive construction in which first the expecte...

As the transition to renewable energy sources progresses, their integration makes electricity production increasingly fluctuating, also causing amplified volatility in electricity prices on energy markets. To contribute to power grid stability, utilities need to balance volatile supply through shifting demand. This measure of demand side management creates flexibility, being enabled as the inte...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...

We describe and experimentally compare three theoretically well-known algorithms for the parallel prefix (or scan, in MPI terms) operation, and give a presumably novel, doubly-pipelined implementation of the in-order binary tree parallel prefix algorithm. Bidirectional interconnects can benefit from this implementation. We present results from a 32 node AMD Cluster with Myrinet 2000 and a 72-no...

Saphenous vein autograft had opened a new erra in revascularization of mycardium in cases with severe angina pectoris. This has attracted the attention of many medical enters so that a rae of 7595% relief of pain has been obtained. 92% of patients have demonstrated sings of cure of choronary iSJChemia and have moved to group 1 from those of group 2, 3, and 4 (dassi­f[ca,tion of American Heart A...

Binomial trees are very popular in both theory and applications of option pricing. As they often suffer from an irregular convergence behavior, improving this is an important task. We build upon a new version of the Edgeworth expansion for lattice models to construct new and quickly converging binomial schemes with a particular application to barrier options.

This paper is concerned with the quantum properties of the binomial model (or, the CRR-model). We show that the single-step binomial model is incomplete in the quantum setting. All risk-neutral states of the single-step binomial model in the quantum setting are characterized. Moreover, it is shown that all single-step models are incomplete in the quantum setting. Therefore, incompleteness is ba...