Two new measures for financial systemic risk are computed based on the time-varying conditional and unconditional probability of simultaneous failures of several financial institutions. These risk measures are derived from a multivariate model that allows for skewed and heavy-tailed changes in...

Modern quantitative theories of international trade rely on the probabilistic representation of technology and the assumption of the Law of Large Numbers (LLN), which ensures that when the number of traded goods goes to infinity, trade flows can be expressed via a deterministic gravity equation...

Abstract This is a short survey about asymptotic properties of a supercritical branching process (Z_{n}) with immigration in a stationary and ergodic or independent and identically distributed random environment. We first present basic properties of the fundamental submartingale (W_{n}) , about...

Nicolas Bernoulli suggested the St Petersburg game, nearly 300 years ago, which is widely believed to produce a paradox in decision theory. This belief stems from a long standing mathematical error in the original calculation of the expected value of the game. This article argues that, in...

Bernoulli’s (1713) well-known Law of Large Numbers (LLN) establishes a legitimate one-way transition from mathematical probability to observed frequency. However, Bernoulli went one step further and abusively introduced the inverse proposition. Based on a careful analysis of Bernoulli’s...

We develop a novel high-dimensional non-Gaussian modeling framework to infer conditional and joint risk measures for many financial sector firms. The model is based on a dynamic Generalized Hyperbolic Skewed-t block-equicorrelation copula with time-varying volatility and dependence parameters...

Modern quantitative theories of international trade rely on the probabilistic representation of technology and the assumption of the Law of Large Numbers (LLN), which ensures that when the number of traded goods goes to infinity, trade flows can be expressed via a deterministic gravity equation...