Gaussian copula is by far the most popular copula used in the financial industry in default dependency modeling. However, it has a major drawback — it does not exhibit tail dependence, a very important property for copula. The essence of tail dependence is the interdependence when extreme events occur, say, defaults of corporate bonds. In this paper we show that some tail dependence can be rest...

Copulas were introduced by Sklar [13] to capture the stochastic dependence structure of random variables. Recall that for n ≥ 2, a function C : [0, 1] → [0, 1] is called an n-dimensional copula (n-copula, for short) whenever it is a restriction of an ndimensional distribution function with all univariate margins uniformly distributed on [0, 1]. Hence an n-copula is characterized by the properties:

Model Renewal processes have been a frequent object of analysis in early studies of stochastic processes, see Cox (1962), for instance. Only recently the idea of parallel renewal processes receives more attention, see Borgelt and Picado-Muino (2012), Gaigalas (2003), Kai et al. (2014), CRC (1994), Kallen et al. (2010), Truccolo (2005), Modir et al. (2010). However, little emphasis has been give...

We investigate the dynamical properties of an associative memory network consisting of stochastic neurons and dynamic synapses that show short-term depression and facilitation. In the stochastic neuron model used in this study, the efficacy of the synaptic transmission changes according to the short-term depression or facilitation mechanism. We derive a macroscopic mean field model that capture...

Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order structure of the volatility, the log returns, as well as their “squares” are discussed in detail. M...

In this paper we present a model of the term structure of interest rates with imperfect information and stochastic differential utility, a form of non-additive recursive utility. A principal feature of recursive utility, that distinguishes it from time-separable expected utility, is its dependence on the timing of resolution of uncertainty. In our model, we parametrize the non-linearity of recu...

Although distance metric learning has been successfully applied to many real-world applications, learning a distance metric from large-scale and high-dimensional data remains a challenging problem. Due to the PSD constraint, the computational complexity of previous algorithms per iteration is at least O(d) where d is the dimensionality of the data. In this paper, we develop an efficient stochas...