<Para ID="Par1">We consider the valuation of options with stressed-beta in a reduced form model. Under this two-state beta model, we provide the analytic pricing formulae for the European options and American options as the integral forms. Specifically, we provide the integral representation of the early...</para>

Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. uniform points on [-1/2,1/2]d, d[greater-or-equal, slanted]2, and for 0p[infinity]. Let L({X1,...,Xn},p) be the total weight of the minimal spanning tree on {X1,...,Xn} with weight function w(e)=ep. Then, there exist strictly positive but finite...

We consider the power laws of certain limiting values in greedy lattice animals which were introduced by Cox, Gandolfi, Griffin, and Kesten (1993) and Gandolfi and Kesten (1994). We study the behavior of the limiting values as we change the parameter p.

In this paper, we study path properties of a d-dimensional Gaussian process with the usual Euclidean norm, via estimating upper bounds of large deviation probabilities on the suprema of the Gaussian process.

Suppose each edge of the complete graph Kn is assigned a random weight chosen independently and uniformly from the unit interval [0,1]. A minimal spanning tree is a spanning tree of Kn with the minimum weight. It is easy to show that such a tree is unique almost surely. This paper concerns the...

Consider the complete graph Kn on n vertices and the n-cube graph Qn on 2n vertices. Suppose independent uniform random edge weights are assigned to each edges in Kn and Qn and let and denote the unique minimal spanning trees on Kn and Qn, respectively. In this paper we obtain the Gaussian tail...

Orban and Wolfe (1982) and Kim (1999) provided the limiting distribution for linear placement statistics under null hypotheses only when one of the sample sizes goes to infinity. In this paper we prove the asymptotic normality and the weak convergence of the linear placement statistics of Orban...

Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. points in , d[greater-or-equal, slanted]2, and let LMM({X1,...,Xn},p), LMST({X1,...,Xn},p), LTSP({X1,...,Xn},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X1,...,Xn} with...

Using the Poisson point process we model how the SiPM works and derive the non-linear response formula of the SiPM. Using this non-linear response formula we are able to capture the mean and variance saturation phenomena near the infinity and the linear behavior of the mean and variance near 0.

In this paper, we establish a martingale inequality and develop the symmetry argument to use this martingale inequality. We apply this to the length of the longest increasing subsequences and the independence number of sparse random graphs.