Giuseppe D'Acquisto

The value of location in keyword auctions

Sponsored links on search engines are an emerging advertising tool, whereby a number of slots are put on sale through keyword auctions. This is also known as contextual advertising. Slot assignment and pricing in keyword auctions are then essential for the search engines management since provide the main stream of revenues, and are typically accomplished by the Generalized Second Price (GSP) mechanism. In GSP the price of slots is a monotone function of the slot location, being larger for the highest slots. Though a higher location is associated with larger revenues, the lower costs associated with the lowest slots may make them more attractive for the advertiser. The contribution of this research is to show, by analytical and simulation results based on the theory of order statistics, that advertisers may not get the optimal slot they aim at (the slot maximizing their expected profit) and that the GSP mechanism may be unfair to all the winning bidders but the one who submitted the lowest bid.

A normal copula model for the economic risk analysis of correlated failures in communications networks

The reliability of a communications network is often evaluated without taking into account the economic consequence of failures. Here a new approach is proposed to assess the economic consequences of failures as a figure of merit of reliable networks. For this purpose a partition of the network operator’s market into service basins is proposed, which includes the presence of correlation between the subsystems needed to serve different service basins as well as within the same service basin. A simulation algorithm, based on the Cross-Entropy method, is fully described to evaluate the probability that the economic loss exceeds a given threshold. An application of the method to a simple scenario is finally reported.

Option pricing in a privacy-aware market

In a privacy-aware market a producer may satisfy the demand by end customers either by producing itself the items or by placing the items provided by privacy-aware suppliers at a reduced price. Price-aware suppliers provide a noisy information about their level of stock. Through an option contract the producer may protect itself against the risk of buying also the excess items delivered by privacy-aware suppliers. We provide a formula for the option price, which is found to be somewhat larger than the cost of the declared excess items.

Information Security Investments: When Being Idle Equals Negligence

The Learned Hands rule, comparing security investments against the expected loss from data breaches, can be used as a simple tool to determine the negligence of the company holding the data. On the other hand, companies may determine their investments in security by maximizing their own net profit. We consider the well known Gordon-Loeb models as well as the more recent Huang-Behara models for the relationship between investments and the probability of money loss due to malicious attacks to determine the outcome of the application of three forms of Hands rule: status quo (loss under no investments), ex-post (loss after investment), transitional (loss reduction due to investment). The company is always held negligent if it does not invest in both the status quo and the transitional form. In the ex-post form, it is instead held negligent just if the potential loss is below a threshold, for which we provide the exact expression.

Influence of Search Neutrality on the Economics of Advertisement-Financed Content

The search neutrality debate questions the ranking methods of search engines. We analyze the issue when content providers offer content for free, but get revenues from advertising. We investigate the noncooperative game among competing content providers under different ranking policies. When the search engine is not involved with high-quality content providers, it should adopt neutral ranking, also maximizing user quality-of-experience. If the search engine controls high-quality content, favoring its ranking and adding advertisement yield a larger revenue. Though user perceived quality may not be impaired, the advertising revenues of the other content providers drastically decrease.

Impact on retail prices of non-neutral wholesale prices for content providers

The impact of wholesale prices is examined in a context where the end customer access both free content and pay-per-use content, delivered by two different providers through a common network provider. We formulate and solve the game between the network provider and the pay-per-use content provider, where both use the price they separately charge the end customer with as a leverage to maximize their profits. In the neutral case (the network provider charges equal wholesale prices to the two content providers), the benefits coming from wholesale price reductions are largely retained by the pay-per-use content provider. When the free content provider is charged more than its pay-per-use competitor, both the network provider and the pay-per-use content provider see their profit increase, while the end customer experiences a negligible reduction in the retail price.

Simulation of Correlated Financial Defaults through Smoothed Cross-Entropy

Credit risk, deriving from borrowers defaulting on their debts, represents an ever growing source of concern for financial operators. An established model to describe the associated risk scenario, where correlation among defaults is present, is the t-copula, whose use allows us to evaluate the probability of losses exceeding a given threshold. However, the typically large number of variables involved calls for a simulation approach. A simulation method, based on the use of the Cross-Entropy (CE) technique, is here proposed as an alternative to non-adaptive Importance Sampling (IS) techniques so far presented in the literature, the main advantage of CE being that it allows to deal easily with a wider range of probability models than ad hoc IS. A full description of the method is provided along with the results obtained for an extended set of model instances. The proposed Cross-Entropy technique is shown to provide accurate results even when the sample size is several orders of magnitude smaller than the inverse of the probability to be estimated.

Computational costs of fast stochastic simulation techniques for Markovian fluid models in multiservice networks

Abstract Two accelerated simulation techniques, Importance Sampling and RESTART, are analyzed in the context of the class of Markovian fluid models, widely used in broadband communication networks. The different terms corresponding to their computational cost are exposed and evaluated for a sample case. Importance Sampling is found to be preferable (i.e. to present the lower computational cost) for the simulation of very rare events and large systems. A tentative criterion is proposed for the a priori selection of the computationally lighter simulation technique, based on the system size and on the probability of the event being estimated.

Solution Space Size in Credit Risk Simulation

In a portfolio of securities, lenders may incur substantial losses if the obligors do not return the money borrowed by them. In credit risk evaluation through simulation, the states of the portfolio associated to large losses are sampled rather than identified exhaustively. Enumeration of all such critical states is however relevant for the early warning of heavy losses. We provide a general enumerative algorithm, and evaluate its computational complexity, which results to be equal to the number of critical states, for three cases of the distribution of losses associated to individual obligors: uniform, linear, and exponential. In the presence of a possibly huge number of critical states, the evaluation of the computational complexity allows us to assess beforehand if the enumeration task is feasible.

Polynomial biasing importance sampling for Markov fluid models

Importance Sampling is an established technique for the simulation of rare events in Markov fluid systems, a widely used model in the context of high-speed multiservice networks. The main issue with Importance Sampling is the definition of the biasing procedure which strongly affects the effectiveness of the simulation technique. In this paper a biasing procedure is proposed which couples the simplicity of application with a performance close to the optimal procedure. The new procedure, named Polynomial Biasing, relies on a single biasing parameter which is used to alter all the elements of the transition rate matrix of the Markov chain with a polynomial sequence. A one-dimensional minimization algorithm is employed to arrive at the best value of the biasing parameter. Polynomial Biasing provides results identical to the optimal biasing for any superposition of two-state sources. For the general case of multi-state sources its performance, analysed through the comparison with the overflow probability obtained through optimal biasing and the evaluation of the optimality indicator in some numerical examples, results close to the optimal one.