We address robust versions of combinatorial optimization problems, focusing on the uncorrelated ellipsoidal uncertainty case, which corresponds to so-called mean-variance optimization. We present a branch and bound-algorithm for such problems that uses lower bounds obtained from Lagrangean decomposition. This approach allows to separate the uncertainty aspect in the objective function from the ...

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for oth...

We show in any economy trading options, with investors having mean-variance preferences, that there are arbitrage opportunities resulting from negative prices for out of the money call options. The theoretical implication of this inconsistency is that mean-variance analysis is vacuous. The practical implications of this inconsistency are investigated by developing an option pricing model for a ...

Abstract.— We describe the use of the Fréchet mean and variance in the Billera-Holmes-Vogtmann (BHV) treespace to summarize and explore the diversity of a set of phylogenetic trees. We show that the Fréchet mean is comparable to other summary methods, despite its stickiness property, and that the Fréchet variance is faster and more precise than commonly used variance measures. These mean and va...

According to the Council of Supply Chain Management Professionals (September 2007), we have the following description for supply chain management: “supply chain management encompasses the planning and management of all activities involved in sourcing and procurement, conversion, and all logistics management activities. Importantly, it also includes coordination and collaboration with channel pa...

This paper studies capital allocation problem based on minimizing loss functions. Two capital allocation models based on the Mean-Variance principle are proposed. General formulas for optimal capital allocations for both models are derived according to quadratic distance measure. In particular, we discuss centrally symmetric distributions and gamma distributions. Some numerical examples are giv...

The aim of the paper is to derive the brand-new estimator for mean and variance that has only numerical approximation. In order to do so the following questions have to be answered: (i) what is the statistical model for the estimation procedure? (ii) what are the properties of the estimator, like optimality (in which class) or asymptotic properties? (iii) how does the estimator work in practice...

We consider the classical Cramér-Lundberg model with dynamic proportional reinsurance and solve the problem of finding the optimal reinsurance strategy which minimizes the expected quadratic distance of the risk reserve to a given benchmark. This result is extended to a mean-variance problem.

Starting from a sample path of a multivariate stochastic process, we study several techniques to isolate linear combinations of the variables with a maximal amount of mean reversion, while constraining the variance of the combination to be larger than a given threshold. We show that many of the optimization problems arising in this context can be solved exactly using semidefinite programming an...

We analyze mean-variance-optimal dynamic hedging strategies in oil futures for oil producers and consumers. In a model for the oil spot and futures market with Gaussian convenience yield curves and a stochastic market price of risk, we find analytical solutions for the optimal trading strategies. An implementation of our strategies in an out-of-sample test on market data shows that the hedging ...