We study a discrete time approximation scheme for the solution of a doubly reflected Backward Stochastic Differential Equation (DBBSDE in short) with jumps, driven by a Brownian motion and an independent compensated Poisson process. Moreover, we suppose that the obstacles are right continuous and left limited (RCLL) processes with predictable and totally inaccessible jumps and satisfy Mokobodzk...

The scattering number of a graph G, denoted sc(G), is defined by sc(G)=max{c(G−S)− |S| : S ⊆ V(G) and c(G−S)≠ 1} where c(G−S) denotes the number of components in G− S. It is one measure of graph vulnerability. In this paper, general results on the scattering number of a graph are considered. Firstly, some bounds on the scattering number are given. Further, scattering number of a binomial tree i...

This note contains two main results. (1) (Discrete time) Suppose S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose the initial option prices agree with the Cox–Ross–Rubinstein binomial tree model.) Then S is a geometric simple random walk. (2) (Continuous time) Suppose S = S0eσX−σ 〈X〉/2 is a cont...

A wide range of graphs with regular structures are shown to be embeddable in an injured hypercube with faulty links. These include rings, linear paths, binomial trees, binary trees, meshes, tori, and many others. Unlike many existing algorithms which are capable of embedding only one type of graphs, our algorithm embeds the above graphs in a uniied way, all centered around a notion called edge ...

The binomial tree method, first proposed by Cox, Ross, and Rubinstein [Journal of Financial Economics, 7 (1979), pp. 229–263], is one of the most popular approaches to pricing options. By introducing an additional path-dependent variable, such methods can be readily extended to the valuation of path-dependent options. In this paper, using numerical analysis and the notion of viscosity solutions...

Lognormal price dynamics and passage to the continuum limit. After a brief recap of our pricing formula, this section introduces the lognormal model of stock price dynamics, and explains how it can be approximated using binomial trees. Then we use these binomial trees to price contingent claims. The Black-Scholes analysis is obtained in the limit δt → 0. As usual, Baxter–Rennie captures the cen...

The pricing models of American-type path-dependent options are of degenerate parabolic obstacle problems. The binomial tree method is the most popular approach to pricing options. For some special cases, this method is modified in order to make it feasible. The main purpose of this paper is, using numerical analysis and the notion of viscosity solutions, to show the uniform convergence of the b...

Let A = {a1, . . . , am} ⊂ Z be a vector configuration and IA ⊂ K[x1, . . . , xm] its corresponding toric ideal. We completely determine the number of different minimal systems of binomial generators of IA. We also prove that generic toric ideals are generated by indispensable binomials. We associate to A a simplicial complex ∆ind(A). We show that the vertices of ∆ind(A) correspond to the indis...

Lognormal price dynamics and passage to the continuum limit. After a brief recap of our pricing formula, this section introduces the lognormal model of stock price dynamics, and explains how it can be approximated using binomial trees. Then we use these binomial trees to price contingent claims. The Black-Scholes analysis is obtained in the limit δt→ 0. As usual, Baxter–Rennie captures the cent...

Modern networks typically limit the size of the largest packet for efficient communication. Thus, long messages are packetized and transmitted. Such networks also provide network interface support for nodes, which typically includes a coprocessor and memory, to implement the lower layers of the communication protocol. This paper presents a concept of smart network interface support for packetiz...