The measurement and the allocation of risk are fundamental problems of portfolio management. Coherent measures of risk provide an axiomatic approach to the former problem. In an environment given by a coherent measure of risk and the various portfolios’ realization vectors, risk allocation games aim at solving the second problem: How to distribute the diversification benefits of the various por...

Sharpe-like ratios have been traditionally used to measure the performances of portfolio managers. However, they are known to suffer major drawbacks. Among them, two are intricate: (1) they are relative to a peer’s performance and (2) the best score is generally assumed to correspond to a “good” portfolio allocation, with no guarantee on the goodness of this allocation. Last but not least (3) t...

Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the posterior...

This paper discusses two optimal allocation problems. We consider different hypotheses of portfolio selection with stable distributed returns for each of them. In particular, we study the optimal allocation between a riskless return and risky stable distributed returns. Furthermore, we examine and compare the optimal allocation obtained with the Gaussian and the stable non-Gaussian distribution...

To obtain the maximum benefits from diversification, financial theory suggests that investors should invest internationally because of the larger potential for risk reduction. The question that we raise in this paper is how to select the optimal portfolio of countries? This article synthesizes the major international asset allocation methods based on mean-variance analysis that have been propos...

Developing a complex software system involves decisions about how to allocate a limited resource budget among a collection of costly software alternatives (such as technologies or analysis techniques) that have uncertain future benefits. Very little quantitative guidance is currently available to make these decisions. We suggest that these allocation problems are naturally viewed in the powerfu...