144 research outputs found
Simple examples of pure-jump strict local martingales
We present simple new examples of pure-jump strict local martingales. The
examples are constructed as exponentials of self-exciting affine Markov
processes. We characterize the strict local martingale property of these
processes by an integral criterion and by non-uniqueness of an associated
ordinary differential equation. Finally we show an alternative construction for
our examples by an absolutely continuous measure change in the spirit of
(Delbaen and Schachermayer, PTRF 1995)
Exponential ergodicity of the jump-diffusion CIR process
In this paper we study the jump-diffusion CIR process (shorted as JCIR),
which is an extension of the classical CIR model. The jumps of the JCIR are
introduced with the help of a pure-jump L\'evy process . Under
some suitable conditions on the L\'evy measure of , we derive a
lower bound for the transition densities of the JCIR process. We also find some
sufficient condition guaranteeing the existence of a Forster-Lyapunov function
for the JCIR process, which allows us to prove its exponential ergodicity.Comment: 14 page
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