The property catastrophe reinsurance industry faces a major challenge. Since 1989, climatic volatility has produced unprecedented insured losses of $43 billion, $18 billion of which were from Hurricane Andrew alone. A surge of insurer defaults and dramatic changes in capacity and pricing have...

In this note we consider a planar network with three bins located at the vertices of an equilateral triangle and customers which are uniformly distributed on the triangle and have Poisson arrival times and general sojourn times. We show that the allocation which minimizes the bin loads and that...

We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the Markov Chain. We apply this result to derive the strong law...

The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. Both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted...

This paper derives a law of large numbers theorem for bifurcating processes defined on a perfect binary tree. This theorem can be viewed as a generalization of some results that have already appeared in the literature. For instance, all that is required of the bifurcating process is an infinite...

Banks increasingly use short-term wholesale funds to supplement traditional retail deposits. Existing literature mainly points to the "bright side" of wholesale funding: sophisticated financiers can monitor banks, disciplining bad but refinancing good ones. This paper models a "dark side" of...

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 consider the optimization problem of a campaign trying to win an election when facing aggregate uncertainty, where agentsʼ voting probabilities are uncertain. Even a small amount of uncertainty will in a large electorate eliminate many of counterintuitive results that arise when voting...

Nabil Al-Najjar (2008) showed how games with countably infinite player sets can be used to approximate games with large finite player sets. Unfortunately, we have found an error in the proof of Al-Najjarʼs Theorem 5. In this correction we discuss the error and offer two slightly weaker versions...

The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the...