Estimation of the Characteristics of the Jumps of a General Poisson-Diffusion Model

Cecilia Mancini

Scandinavian Actuarial Journal, 2004, vol. 2004, issue 1, 42-52

Abstract: We consider a filtered probability space with a standard Brownian motion W, a simple Poisson process N with constant intensity λ>0, and we consider the process Y such that Y0∈ℝ and where a, σ are predictable bounded stochastic processes, and γ is a predictable process which is bounded away from zero. A discrete record of n+1 observations {Y0, Yt1, …, Ytn−1, Ytn} is available, with ti=ih. Using such observations, we construct estimators of Nti, i=1, …, n, λ and γτj, where τj are the instants of jump within [0, nh]. They are consistent and asymptotically controlled when the number of observations increases and the step h tends to zero.

Date: 2004
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DOI: 10.1080/034612303100170091

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