Affine Point Processes: Approximation and Efficient Simulation

Affine Point Processes: Approximation and Efficient Simulation

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Affine Point Processes and Portfolio Credit Risk

This paper analyzes a family of multivariate point process models of correlated event timing whose arrival intensity is driven by an affine jump diffusion. The components of an affine point process are selfand cross-exciting, and facilitate the description of complex event dependence structures. Ordinary differential equations characterize the transform of an affine point process and the probab...

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Pricing Credit from the Top down with Affine Point Processes

A portfolio credit derivative is a contingent claim on the aggregate loss of a portfolio of credit sensitive securities. We develop an economically motivated and computationally tractable top down valuation framework in which portfolio loss follows an affine point process. The magnitude of each loss is random and defaults are governed by an intensity that is driven by affine jump diffusion risk...

Perfect Simulation for Spatial Point Processes