A note on the split rank of intersection cuts

In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that ! log 2(l)mixed integer programming, split rank, intersection cuts.

Adding independent risks in an insurance portfolio: which shape for the insurers’ preferences?

Many papers in the litterature have adopted the expected utility paradigm to analyze insurance decisions. Insurance companies manage policies by growing, by adding independent risks. Even if adding risks generally ultimately decreases the probability of insolvency, the impact on the insurer's expected utility is less clear. Indeed, it is not true that the risk aversion toward the additional loss generated by a new policy included in an insurance portfolio is a decreasing function of the number of contracts already underwritten (i.e. the "fallacy of large numbers"). In this paper, it is shown that most commonly used utility functions do not necessarily positively value the aggregation of independent risks so that they are not éligible for insurers. This casts some doubt about the conclusions drawn in the papers postulating such completely monotonic utilities for guiding insurers' choices. Finally, it is shown that the sufficient conditions for adding risks that can be found in the litterature need to be refined by restricting the domain of definition of the insurer's utility function.expected utility, compensating premium, prudence, temperance

Approximate level method

In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the feasible region and a polyhedron arising as a level set of the model. We show that by replacing exact computations in both cases by approximate computations, in relative scale, the theoretical iteration complexity increases only by the factor of four. This means that while spending less work on the subproblems, we are able to retain the good theoretical properties of the level method.evel method, approximate projections in relative scale, nonsmooth convex optimization, sensitivity analysis, large-scale optimization.

Estimating autocorrelations in the presence of deterministic trends

This paper considers the impact of ordinary least squares (OLS) detrending and the first difference (FD) detrending on autocorrelation estimation in the presence of long memory and deterministic trends. We show that the FD detrending results in inconsistent autocorrelation estimates when the error term is stationary. Thus, the FD detrending should not be employed for autocorrelation estimation of the detrended series when constructing e.g. portmanteau-type tests. In an empirical application of volume in Dow Jones stocks, we show that for some stocks, OLS and FD detrending result in substantial differences in ACF estimates.autocorrelations, OLS, first difference detrending, long memory.

Public goods’ attractiveness and migrations

The aim of this paper is to develop a dynamic model of migrations, in which migration is driven by size asymmetries between countries and by the relative preferences of consumers between private consumption and consumption of public goods. The dynamic trajectories heavily depend on the degree of attractiveness for public goods We show that monotone migrations require sufficiently strong preferences for public goods, and can only be sustained from the small to the large countries. We identify the threshold value of the public goods’ intensity of preferences guaranteeing the survival of the small country. For weaker preference intensities, oscillating migrations may arise, but they finally converge to situation where both countries are of equal size.migration, public goods, income tax.

Correlated risks, bivariate utility and optimal choices

In this paper, we consider a décision-maker facing a financial risk flanked by a background risk, possibly non-financial, such as health or environmental risk. A decision has to be made about the amount of an investment (in the financial dimension) resulting in a future benefit either in the same dimension (savings) or in the order dimension (environmental quality or health improvement). In the first case, we show that the optimal amount of savings decreases as the pair of risks increases in the bivariate increasing concave dominance rules of higher degrees which express the common preferences of all the decision-makers whose two-argument utility function possesses direct and cross derivatives fulfilling some specific requirements. Roughly speaking, the optimal amount of savings decreases as the two risks become "less positively correlated" or marginally improve in univariate stochastic dominance. In the second case, a similar conclusion on optimal investment is reached under alternative conditions on the derivatives of the utility function.bivariate higher order increasing concave stochastic dominance, precautionary savings, background risk, dependence

The role of Skorokhod space in the development of the econometric analysis of time series

This paper discusses the fundamental role played by Skorokhod space, through its underpinning of functional central limit theory, in the development of the paradigm of unit roots and co-integration. This paradigm has fundamentally affected the way economists approach economic time series as was recognized by the award of the Nobel Memorial Prize in Economic Sciences to Robert F. Engle and Clive W.J. Granger in 2003. Here, we focus on how P.C.B. Phillips and others used the Skorokhod topology to establish a limiting distribution theory that underpinned and facilitated the development of methods of estimation and testing of single equations and systems of equations with possibly integrated regressors. This approach has spawned a large body of work that can be traced back to Skorokhod's conception of fifty years ago. Much of this work is surprisingly confined to the econometrics literature.Skorokhod space, functional central limit theorems, non-stationary time series, unit roots and co-integration, Wiener functionals, econometrics.

Technological breakthroughs and asset replacement

The authors analyze the optimal replacement of assets under continuous and discontinuous technological change. They investigate the variable lifetime of assets in an infinite-horizon replacement problem. Due to deterioration, the maintenance cost increases when the asset becomes older. Because of technological change, both maintenance and new capital costs decrease for a fixed asset age. The dynamics of the optimal lifetime is investigated analytically and numerically under technological change in the cases of one and several technological breakthroughs. It is shown that the breakthroughs cause irregularities (anticipation echoes) in the asset lifetime before the breakthrough time.asset replacement, technological change, optimal lifetime, anticipation echoes.

A viability theory approach to a two-stage optimal control problem of technology adoption

A new technology adoption problem can be modelled as a two-stage control problem, in which model parameters ("technology") might be altered at some time. An optimal solution to utility maximisation for this class of problems needs to contain information on the time, at which the change will take place (0, finite or never), along with the optimal control strategies before and after the change. For the change, or switch, to occur the "new technology" value function needs to dominate the "old technology" value function, after the switch. We charaterise the value function using the fact that its hypograph is a viability kernel of an auxiliary problem and we study when the graphs can intersect. If they do not, the switch cannot occur at a positive time. Using this characterisation we analyse a technology adoption problem and showmodels, for which the switch will occur at time zero or never.technology adoption, value function, viability kernel, viscosity solutions