TITLE:
The Existence and Uniqueness of Solutions for Mean-Reverting γ-Process
AUTHORS:
Jiyuan Liao
KEYWORDS:
Mean-Reverting γ-Process, Existence and Uniqueness, Non-Negative
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.2,
April
24,
2018
ABSTRACT: Empirical studies show that more and more short-term
rate models in capturing the dynamics cannot be described by those classic ones.
So the mean-reverting γ-process was
correspondingly proposed. In most cases, its coefficients do not satisfy the
linear growth condition; even they satisfy the local Lipschitz condition. So we
still cannot examine its existence of solutions by traditional techniques. This
paper overcomes these difficulties. Firstly, through using the function Lyapunov,
it has proven the existence and uniqueness of solutions for mean-reverting γ-process when the parameter . Secondly, when , it proves the solution is non-negative. Finally,
it proves that there is a weak solution to the mean-reverting γ-process and the solution satisfies the
track uniqueness by defining a function ρ.
Therefore, the mean-reverting γ-process
has the unique solution.