Geoffrey Decrouez

Jump-diffusion modeling in emission markets

Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate the fair prices of such financial products, one needs appropriate models for the evolution of the underlying assets, emission allowance certificates. In this paper, we discuss continuous time diffusion and jump-diffusion models, the latter enabling one to model information shocks that cause jumps in allowance prices. We show that the resulting martingale dynamics can be described in terms of non-linear partial differential and integro-differential equations and use a finite difference method to investigate numerical properties of their discretizations. The results are illustrated by a small numerical study.

A CLASS OF MULTIFRACTAL PROCESSES CONSTRUCTED USING AN EMBEDDED BRANCHING PROCESS

We present a new class of multifractal process on R, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the boundaries of multitype Galton–Watson trees. Our class of processes includes Brownian motion subjected to a continuous multifractal time-change. In addition, if we observe our process at a fixed spatial resolution, then we can obtain a finite Markov representation of it, which we can use for on-line simulation. That is, given only the Markov representation at step n, we can generate step n+ 1 in O(logn) operations. Detailed pseudo-code for this algorithm is provided.

Normal approximation and smoothness for sums of means of lattice-valued random variables

Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the main effects of distribution smoothness can be understood in terms of the ratio

Galton Watson Fractal Signals

\rho_{12}=(e_2n_1)/(e_1n_2)

Analysis of H-sssi processes using the crossing tree: An alternative to wavelets

, where

Time-series models for border inspection data.

e_1

Bias‐Corrected Estimation in Continuous Sampling Plans

and

Crossing-tree partition functions

e_2

Ornstein--Uhlenbeck Type Processes with Heavy Distribution Tails

are the respective maximal lattice edge widths of the two populations, and

Galton?Watson iterated function systems

n_1