Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model

In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always result in the best rate of return on assets. Prior to making investment decisions, it is important to an investor to know the potential minimal investment risk (or the expected minimal investment risk) and to determine the strategy that will maximize the return on assets. We use the self-averaging property to analyze the potential minimal investment risk and the concentrated investment level for the strategy that gives the best rate of return. We compare the results from our method with the results obtained by the operations research approach and with those obtained by a numerical simulation using the optimal portfolio. The results of our method and the numerical simulation are in agreement, but they differ from that of the operations research approach.Comment: 37 pages, 1 figur

A Lightweight Distributed Solution to Content Replication in Mobile Networks

Performance and reliability of content access in mobile networks is conditioned by the number and location of content replicas deployed at the network nodes. Facility location theory has been the traditional, centralized approach to study content replication: computing the number and placement of replicas in a network can be cast as an uncapacitated facility location problem. The endeavour of this work is to design a distributed, lightweight solution to the above joint optimization problem, while taking into account the network dynamics. In particular, we devise a mechanism that lets nodes share the burden of storing and providing content, so as to achieve load balancing, and decide whether to replicate or drop the information so as to adapt to a dynamic content demand and time-varying topology. We evaluate our mechanism through simulation, by exploring a wide range of settings and studying realistic content access mechanisms that go beyond the traditional assumptionmatching demand points to their closest content replica. Results show that our mechanism, which uses local measurements only, is: (i) extremely precise in approximating an optimal solution to content placement and replication; (ii) robust against network mobility; (iii) flexible in accommodating various content access patterns, including variation in time and space of the content demand.Comment: 12 page

Exploring heterogeneity of unreliable machines for p2p backup

P2P architecture is a viable option for enterprise backup. In contrast to dedicated backup servers, nowadays a standard solution, making backups directly on organization's workstations should be cheaper (as existing hardware is used), more efficient (as there is no single bottleneck server) and more reliable (as the machines are geographically dispersed). We present the architecture of a p2p backup system that uses pairwise replication contracts between a data owner and a replicator. In contrast to standard p2p storage systems using directly a DHT, the contracts allow our system to optimize replicas' placement depending on a specific optimization strategy, and so to take advantage of the heterogeneity of the machines and the network. Such optimization is particularly appealing in the context of backup: replicas can be geographically dispersed, the load sent over the network can be minimized, or the optimization goal can be to minimize the backup/restore time. However, managing the contracts, keeping them consistent and adjusting them in response to dynamically changing environment is challenging. We built a scientific prototype and ran the experiments on 150 workstations in the university's computer laboratories and, separately, on 50 PlanetLab nodes. We found out that the main factor affecting the quality of the system is the availability of the machines. Yet, our main conclusion is that it is possible to build an efficient and reliable backup system on highly unreliable machines (our computers had just 13% average availability)