arXiv subjects

Patrice Takam Soh

Publications and source records attributed to Patrice Takam Soh.

3 recordsLinked to original sources

arXiv2021

Perturbations of copulas and Mixing properties

This paper explores the impact of perturbations of copulas on the dependence properties of the Markov chains they generate. We consider Markov chains generated by perturbed copulas. Results are provided for the mixing coefficients $β_n$, $ψ_n$ and $ϕ_n$. Several results are provided on mixing for the considered perturbations. New copula functions are provided in connection with perturbations of variables that induce other types of perturbation of copulas not considered in the literature.

math.PR↗

arXiv2019

European Option Pricing of electricity under exponential functional of Lévy processes with Price-Cap principle

We propose a new model for electricity pricing based on the price cap principle. The particularity of the model is that the asset price is an exponential functional of a jump Lévy process. This model can capture both mean reversion and jumps which are observed in electricity market. It is shown that the value of an European option of this asset is the unique viscosity solution of a partial integro-differential equation (PIDE). A numerical approximation of this solution by the finite differences method is provided. The consistency, stability and convergence results of the scheme are given. Numerical simulations are performed under a smooth initial condition.

q-fin.PR↗

arXiv2017

Weak decreasing stochastic order

We introduce the notion of weak decreasing stochastic (WDS) ordering for real-valued processes with negative means, which, to our knowledge, has not been studied before. Thanks to Madan-Yor's argument, it follows that the WDS ordering is a necessary and sufficient condition for a process with negative mean to be embeddable in a standard Brownian motion by the Cox and Hobson extension of the Azéma-Yor algorithm. Since the decreasing stochastic order is stronger than the WDS order, then, for every stochastically non-decreasing family of probability measures with densities, the Cox-Hobson stopping times provide an associated Markov process. The quantile process associated to a stochastically non-decreasing process is not necessarily Markovian.

math.PR↗