Given a portfolio of risks, we study the marginal behavior of the ith risk under an adverse event, such as an unusually large loss in the portfolio or, in the case of a portfolio with a positive dependence structure, to an unusually large loss for another risk. By considering some particular...

Sarkar (1998) showed that certain positively dependent (MTP2) random variables satisfy the Simes inequality. The multivariate-t distribution does not satisfy this (MTP2) property, so other means are necessary. A corollary was given in Sarkar (1998) to handle this distribution, but there is an...

Considering the covariance selection problem of multivariate normal distributions, we show that its Fenchel dual formulation is insightful and allows one to calculate direct estimates under decomposable models. We next generalize the covariance selection to multivariate dependence, which...

By the Fourier filtering method, we generate one-dimensional binary sequences from coarse-grained continuous sequences with preset exponents α0. Using the spectrum analysis, we find that the corresponding binary sequences have pure 1/fα power spectrum and spectrum exponents α∈[0.0,2.0],...

We propose a complex quantity, AL, to characterize the degree of disorder of L-length binary symbolic sequences. As examples, we respectively apply it to typical random and deterministic sequences. One kind of random sequences is generated from a periodic binary sequence and the other is...

To pass from a deterministic dynamics of aggregate quantities to a probabilistic dynamics of a system of microvariables that describe the individual strategies of a population of economic agents, the route is that of Boltzmann’s kinetic theory at the half of XIX century (more suitable than...

The paper outlines an exchangeable non-Bayesian model of preference generalizing the Savage/de Finetti classic model of subjective expected utility preference with an exchangeable prior. The treatment is informal, and the emphasis is on motivation and potential applications rather than on...