This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility – in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the...

The usual derivation of the Fokker-Planck partial differential eqn. (pde) assumes the Chapman-Kolmogorov equation for a Markov process [1,2]. Starting instead with an Ito stochastic differential equation (sde), we argue that finitely many states of memory are allowed in Kolmogorov’s two pdes,...

We show that Ito processes imply the Fokker-Planck (K2) and Kolmogorov backward time (K1) partial differential eqns. (pde) for transition densities, which in turn imply the Chapman-Kolmogorov equation without approximations. This result is not restricted to Markov processes. We define ‘finite...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the...

It is well known that the traditional estimated risk for the Markowitz mean-variance optimization had been demonstrated to seriously depart from its theoretic optimal risk due to accumulation of input estimation errors. Fan et al. (in J. Am. Stat. Assoc. 107:592–606, <CitationRef CitationID="CR4">2012a</CitationRef>) addressed the...</citationref>

In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, and their asymptotic properties are studied. Our proposed estimator is compared with the existing...

This paper derives optimal pricing strategies for nondurables if demand is sluggish and stochastic. The puzzling result is that moving from a static demand to a dynamic relation alters the marketing strategy dramatically if the equilibrium demand is convex (in price): the profit maximizing price...