相关论文: Asymptotic distribution of the Markowitz portfolio
In this paper, we develop modified versions of the likelihood ratio test for multivariate heteroskedastic errors-in-variables regression models. The error terms are allowed to follow a multivariate distribution in the elliptical class of…
Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz's Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most…
For a reversible and ergodic Markov chain $\{X_n,n\geq0\}$ with invariant distribution $\pi$, we show that a valid confidence interval for $\pi(h)$ can be constructed whenever the asymptotic variance $\sigma^2_P(h)$ is finite and positive.…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
A new four-parameter model called the Marshall-Olkin extended generalized Gompertz distribution is introduced. Its hazard rate function can be constant, increasing, decreasing, upside-down bathtub or bathtub-shaped depending on its…
Sufficient conditions are provided under which the log-likelihood ratio test statistic fails to have a limiting chi-squared distribution under the null hypothesis when testing between one and two components under a general two-component…
We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexity while preserving full covariance information. Inspired by…
We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio…
In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems…
A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…
This paper considers the asymptotic properties of the recursive maximum likelihood estimation in hidden Markov models. The paper is focused on the asymptotic behavior of the log-likelihood function and on the point-convergence and…
This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…
We review some fundamental concepts of investment from a mathematical perspective, concentrating specifically on fractional-Kelly portfolios, which allocate a fraction of wealth to a growth-optimal portfolio while the remainder collects (or…
Hamiltonian Monte Carlo (HMC) is a Markov chain algorithm for sampling from a high-dimensional distribution with density $e^{-f(x)}$, given access to the gradient of $f$. A particular case of interest is that of a $d$-dimensional Gaussian…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $\pi$ defined on a space $(\Theta,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{\theta_{n},n\geq1\}$ of invariant distribution…
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…
Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…
Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…