Abstract integration of set-valued functions

We develop an abstract notion of integration for Effros measurable correspondences whose values are weakly compact subsets of a separable Banach space. This notion is built on a basic monotonicity hypothesis and the simple requirements that the integral assigns at most one value to any single-valued correspondence and evaluates the constant functions in the obvious way; linearity of the integral is not required. These hypotheses alone guarantee that the abstract integral is relatively weakly compact-valued, and its closed convex hull decomposes into the abstract integrals of the measurable selections from that correspondence. We use this decomposition theorem to prove a Fatou-type lemma and a monotone convergence theorem, and to derive necessary and sufficient conditions for the linearity and parametric continuity of the abstract integral. In turn, we apply our main results to obtain simple characterizations of some classical set-valued integrals, and derive (possibly nonadditive) aggregation methods for correspondences. All in all, we find that abstract integration theory yields many results about particular integrals for set-valued maps in a unified manner, often with minimal recourse to measure-theoretic arguments

Enriched Pitman–Yor processes

Bayesian non-parametrics has evolved into a broad area encompassing flexible methods for Bayesian inference, combinatorial structures, tools for complex data reduction, and more. Discrete prior laws play an important role in these developments, and various choices are available nowadays. However, many existing priors, such as the Dirichlet process, have limitations if data require nested clustering structures. Thus, we introduce a discrete non-parametric prior, termed the enriched Pitman–Yor process, which offers higher flexibility in modeling such elaborate partition structures. We investigate the theoretical properties of this novel prior and establish its formal connection with the enriched Dirichlet process and normalized random measures. Additionally, we present a square-breaking representation and derive closed-form expressions for the posterior law and associated urn schemes. Furthermore, we demonstrate that several established models, including Dirichlet processes with a spike-and-slab base measure and mixture of mixtures models, emerge as special instances of the enriched Pitman–Yor process, which therefore serves as a unified probabilistic framework for various Bayesian non-parametric priors. To illustrate its practical utility, we employ the enriched Pitman–Yor process for a species-sampling ecological problem

Machine learning-assisted health economics and policy reviews: a comparative assessment

Introduction: The growth of scientific literature in health economics and policy represents a challenge for researchers conducting literature reviews. This study explores the adoption of a machine learning (ML) tool to enhance title and abstract screening. By retrospectively assessing its performance against the manual screening of a recent scoping review, we aimed to evaluate its reliability and potential for streamlining future reviews. Methods: ASReview was utilised in 'Simulation Mode' to evaluate the percentage of relevant records found (RRF) during title/abstract screening. A dataset of 10,246 unique records from three databases was considered, with 135 relevant records labelled. Performance was assessed across three scenarios with varying levels of prior knowledge (PK) (i.e., 5, 10, or 15 records), using both sampling and heuristic stopping criteria, with 100 simulations conducted for each scenario. Results: The ML tool demonstrated strong performance in facilitating the screening process. Using the sampling criterion, median RRF values stabilised at 97% with 25% of the sample screened, saving reviewers approximately 32 working days. The heuristic criterion showed similar median values, but greater variability due to premature conclusions upon reaching the threshold. While higher PK levels improved early-stage performance, the ML tool's accuracy stabilised as screening progressed, even with minimal PK. Conclusions: This study highlights the potential of ML tools to enhance the efficiency of title and abstract screening in health economics and policy literature reviews. To fully realise this potential, it is essential for regulatory bodies to establish comprehensive guidelines that ensure ML-assisted reviews uphold rigorous evidence quality standards, thereby enhancing their integrity and reliability

Analyzing the concept of loyalty. A four-dimensional relationship with the brand

Companies that successfully implement targeted, adaptive loyalty strategies not only boost customer retention but are better positioned to grow and thrive over the long term. The ability to understand the various aspects that influence customer loyalty is essential to creating programs that effectively address consumer needs. To do this, we need to analyze the four main dimensions of loyalty: cognitive, affective, conative, and behavioral. These dimensions reflect various aspects of the relationship between the customer and the brand, so for each one, we must identify the key antecedents (the factors that cause its occurrence) and outcomes (the concrete effects that arise)

Essays on Information in Frictional Labor Markets

This dissertation comprises three essays centered around the role of subjective expectations in labor markets. In equilibrium search models of the labor market, processes such as wage formation, job creation, offer acceptance, among others, largely depend on agents’ expectations. Throughout these essays, I research how workers form expectations about aggregate and idiosyncratic factors that determine their behavior, with an emphasis on job search. In the first chapter, I quantify the pass-through from inflation expectations to job search behavior by designing and implementing a survey of United States workers. The second chapter studies whether workers’ perceived unemployment risk (i.e. their beliefs about job loss) responds to public information about mass lay-offs. The last chapter empirically contrasts individuals’ job loss beliefs with their realized employment outcomes and investigates how overestimation of unemployment risk affects on-the-job search decisions. Overall, this thesis shows that workers’ expectations about the idiosyncratic and aggregate risk they face predicts their decisions in the labor market. Workers incorporate information about local idiosyncratic events and other macroeconomic variables, such as inflation, when forming expectations about future unemployment. There is vast heterogeneity in expectations, which is only partially explained by factors such as demographics, job related characteristics or location. Together, the chapters in this dissertation provide foundations for future research on various fronts, such as the design of optimal unemployment insurance or employment protection policies, as well as how Central Bank communication can be used as a tool for expectations’ management

American options with liquidation penalties

This paper integrates liquidation costs into the pricing of American options in an arbitrage-free and otherwise frictionless market. The introduction of liquidation penalties changes the comparison between immediate payoff and continuation value for American option holders. Without these penalties, the continuation value is equal to the actual funds obtainable by selling the option. When the sale proceeds achievable upon liquidation are lower due to penalties, immediate exercise becomes more advantageous, leading to a wider optimal early exercise region. We start studying the impact of liquidation penalties in discrete time, and provide closed-form solutions for perpetual American call options in the binomial model. In the continuous-time lognormal model, we derive closed-form asymptotic solutions near maturity for the critical price that triggers optimal early exercise. We also provide explicit pricing formulas for perpetual American options with liquidation penalties. Our results are relevant for executive stock options (ESOs), which typically exhibit liquidation penalties, and for the American equity options for which there is evidence of liquidation costs

Subtle Cues and Substantial Challenges in Early-Stage Financing: Essays on Pitch Evaluation and Women in Entrepreneurship

This dissertation primarily address scholarly conversations on (1) communication strategy in entrepreneurial pitches and (2) the inclusivity of women in entrepreneurship, in both formal and informal early-stage financing settings. Empirically, I employ machine learning algorithms to analyze large unstructured data, including texts, images, and videos of entrepreneurs collected from publicly accessible websites like YouTube and Kickstarter. I also refer to large scale archival database of funding deal records from Crunchbase. Recognizing the challenge in quantifying subtle nonverbal cues within entrepreneurial pitches, my dissertation began with a comprehensive review of coding tools used in published social science papers, complemented by practical applications to 50 accelerator pitch videos. This study wraps up with targeted algorithm suggestions for facial and vocal analysis, alongside a qualitative discussion about emotional disclosure in accelerator pitches of successful entrepreneurs. Transitioning from methodological exploration to practical application, the next study analyzed 183 pitch videos to uncover gender differences in the evaluation of nonverbal emotional neutrality in the crowdfunding context. I observed that gender-conforming expressions of emotion tend to be favored over non-conforming ones among informal investors. Building on these insights about gender difference in early-stage financing evaluation, the third study examines a potential solution to early-stage funding access of female entrepreneurs. Contrary to the implications of gender homophily between female investors and entrepreneurs, I find that the representation of female-founded startups securing initial funding rounds decreased when a female venture capitalist is involved, in states with heightened public attention post Elizabeth Holmes scandal. Overall, this dissertation critically explores gender and entrepreneurship, focusing on the subtle cues that may benefit women in pitch evaluations and substantial challenges they face in securing early-stage financing

La pena come ‘contraccambio’? Qualche riflessione su fondamenti e scopi della pena nella prospettiva del diritto costituzionale

La pena è tradizionalmente considerata come ‘giusta reazione’ al reato: come, cioè, «contraccambio»1 del male che l’autore ha causato alla vittima e alla società tutta mediante la commissione del reato. Questo è il senso, d’altronde, della legge del taglione: il male della pena è una risposta, il più possibile omogenea, al male causato dal reato. Chi ha ucciso merita egli stesso la medesima sorte della sua vittima. L’art. 27, terzo comma, Cost. apre però a una prospettiva tutta diversa: quella di una pena non solo conforme al senso di umanità, ma anche finalisticamente orientata alla ‘rieducazione’ del condannato. Una pena, dunque, non più funzionale alla punizione del reo, intesa come intenzionale inflizione di una sofferenza per una finalità di espiazione del male provocato; ma come cammino orientato a stimolare un cambiamento nella persona del reo, affinché si astenga in futuro dal commettere altri reati. Di qui la domanda, attorno alla quale ruoterà la mia piccola riflessione odierna: può davvero affermarsi che l’avvento della Costituzione, e del terzo comma dell’art. 27 in particolare, abbia segnato il definitivo superamento della concezione retributiva della pena2, imponendo – con la forza della legge suprema della Repubblica – un modello di pena esclusivamente orientato alla prevenzione speciale positiva