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Closed-form likelihood expansions for multivariate diffusions. (English) Zbl 1246.62180

Summary: This paper provides closed-form expansions for the log-likelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial statistics and Monte Carlo evidence are included, along with the convergence of the expansion to the true likelihood function.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
65C05 Monte Carlo methods
62P05 Applications of statistics to actuarial sciences and financial mathematics

Software:

stochastic
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