Assumptions about the dynamic and distributional behavior of risk factors are crucial for the construction of optimal portfolios and for risk assessment. Although asset returns are generally characterized by conditionally varying volatilities and fat tails, the normal distribution with constant variance continues to be the standard framework in portfolio management. Here we propose a practical ...

Under the assumption of the Riemann hypothesis, the Linear Independence hypothesis, and a bound on negative discrete moments of the Riemann zeta function, we prove the existence of a limiting logarithmic distribution of the normalisation of the weighted sum of the Liouville function, Lα(x) = ∑ n≤x λ(n)/n α, for 0 ≤ α < 1/2. Using this, we conditionally show that these weighted sums have a negat...

We introduce a new digital signature model, called conditionally verifiable signature (CVS), which allows a signer to specify and convince a recipient under what conditions his signature would become valid and verifiable; the resulting signature is not publicly verifiable immediately but can be converted back into an ordinary one (verifiable by anyone) after the recipient has obtained proofs, i...

Markov switching models can be used to study heterogeneous populations that are observed over time. This paper explores modeling the group characteristics nonparametrically, under both homogeneous and nonhomogeneous Markov switching for group probabilities. The model formulation involves a finite mixture of conditionally independent Dirichlet process mixtures, with a Markov chain defining the m...

Gini index is a widely used measure of economic inequality. This article develops a theory and methodology for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width without assuming any specific distribution of the data. Fixed sample size methods cannot simultaneously achieve both specified confidence coefficient and fixed width. We deve...

A standard approach to the fitting of stochastic mortality models is to maximise a likelihood function underpinned by an assumption that deaths follow a conditionally independent Poisson distribution. This, in turn, has led researchers to develop increasingly complex models in an effort to improve in-sample explanatory power. This paper, using the Cairns-BlakeDowd (CBD) model as an example, pro...

This article introduces a new Bayesian approach to the analysis of right-censored survival data. The hazard rate of interest is modeled as a product of conditionally independent stochastic processes, corresponding to (1) a baseline hazard function, and (2) a regression function representing the temporal innuence of the covariates. These processes jump at times that form time-homogeneous Poisson...