Andreas Nordvall Lagerås

Copulas for Markovian dependence

Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper demonstrates some di ...Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper shows some difficulties with using copulas even for Markov processes: some tractable copulas such as mixtures between copulas of complete coand countermonotonicity and independence (Fréchet copulas) are shown to imply quite a restricted type of Markov process, and Archimedean copulas are shown to be incompatible with Markov chains. We also investigate Markov chains that are spreadable, or equivalently, conditionally i.i.d.

Strategic complementarities, network games and endogenous network formation

This paper investigates the role of strategic complementarities in the context of network games and network formation models. In the general model of static games on networks, we characterize conditions on the utility function that ensure the existence and uniqueness of a pure-strategy Nash equilibrium, regardless of the network structure. By applying the game to empirically-relevant networks that feature nestedness—Nested Split Graphs—we show that equilibrium strategies are non-decreasing in the degree. We extend the framework into a dynamic setting, comprising a game stage and a formation stage, and provide general conditions for the network process to converge to a Nested Split Graph with probability one, and for this class of networks to be an absorbing state. The general framework presented in the paper can be applied to models of games on networks, models of network formation, and combinations of the two.

Central limit theorems for contractive Markov chains

We prove limit theorems for Markov chains under (local) contraction conditions. As a corollary we obtain a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities.

Commutation functions under Gompertz–Makeham mortality

It is known, but perhaps not well-known, that when the mortality is assumed to be of Gompertz–Makeham-type, the expected remaining life-length and the commutation functions used for calculating the expected values of various types of life insurances can be expressed with an incomplete gamma function with a negative shape parameter. This is not of much use if ones software cannot calculate these values. The aim of this note is to show that one can express the commutation functions using only the exponential function, the (ordinary) gamma function and the gamma distribution function, which are all implemented in common statistical and spreadsheet software. This eliminates the need to evaluate the commutation functions and expected remaining life-length with numerical integration.