Nakahiro Yoshida

Asymptotic expansions of maximum likelihood estimators for small diffusions via the theory of Malliavin-Watanabe

SummaryThe asymptotic expansions of the probability distributions of statistics for the small diffusion are derived by means of the Malliavin calculus. From this the second order efficiency of the maximum likelihood estimator is proved.

Information Criteria in Model Selection for Mixing Processes

We present information criteria for statistical model evaluation problems for stochastic processes. The emphasis is put on the use of the asymptotic expansion of the distribution of an estimator based on the conditional Kullback–Leibler divergence for stochastic processes. Asymptotic properties of information criteria and their improvement are discussed. An application to a diffusion process is presented.

Asymptotic Expansion for Small Diffusions Applied to Option Pricing

Using the Malliavin calculus, we derive asymptotic expansion of the distribution of statistics related to small diffusions. Applications to option pricing in economics are presented.

Asymptotic expansion of Bayes estimators for small diffusions

SummaryUsing the Malliavin calculus we derived asymptotic expansion of the distributions of the Bayes estimators for small diffusions. The second order efficiency of the Bayes estimator is proved.

Estimation of the lead-lag parameter from non-synchronous data

We propose a simple continuous time model for modeling the lead-lag effect between two financial assets. A two-dimensional process

Asymptotic expansion formulas for functionals of ε-Markov processes with a mixing property

(X_t,Y_t)

Conditional expansions and their applications

reproduces a lead-lag effect if, for some time shift

Asymptotic behavior of M-estimator and related random field for diffusion process

\vartheta\in \mathbb{R}

Malliavin calculus and martingale expansion

, the process

Second-order asymptotic expansion for a non-synchronous covariation estimator

(X_t,Y_{t+\vartheta})