A Generalized Normal Mean Variance Mixture for Return Processes in Finance

A Generalized Normal Mean Variance Mixture for Return Processes in Finance

Time-changed Brownian motions are extensively applied as mathematical models for asset returns in Finance. Time change is interpreted as a switch to trade-related business time, different from calendar time. Time-changed Brownian motions can be generated by infinite divisible normal mixtures. The standard multivariate normal mean variance mixtures assume a common mixing variable. This correspon...

Mixture of Normal Mean-Variance of Lindley Distributions

‎Abstract: In this paper, a new mixture modelling using the normal mean-variance mixture of Lindley (NMVL) distribution has been considered. The proposed model is heavy-tailed and multimodal and can be used in dealing with asymmetric data in various theoretic and applied problems. We present a feasible computationally analytical EM algorithm for computing the maximum likelihood estimates. T...

Screening for a Multivariate Mixture Normal Distribution

CONSISTENCY OF PENALIZED MLE FOR NORMAL MIXTURES IN MEAN AND VARIANCE Running Title: Consistency of Estimates in Normal Mixture By

The finite mixture of normal distributions in both mean and variance parameters have wide applications. It is well known that the likelihood function of this model is unbounded for any given sample size. Hence, the ordinary maximum likelihood estimator is not consistent. At the same time, a local maximum of the likelihood function can often be found to have good statistical properties. In this ...

Mean-Variance Optimization in Markov Decision Processes

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for oth...