How to allocate limited resources to projects that will yield the greatest long-term benefits is a problem that often arises in decision-making under uncertainty. For example, organizations may need to evaluate and select innovation projects with risky returns. Similarly, when allocating resources to research projects, funding agencies are tasked with identifying the most promising proposals based on idiosyncratic criteria. Finally, in participatory budgeting, a local community may need to select a subset of public projects to fund. Regardless of context, agents must estimate the uncertain values of a potentially large number of projects. Developing parsimonious methods to compare these projects, and aggregating agent evaluations so that the overall benefit is maximized, are critical in assembling the best project portfolio. Unlike in standard sorting algorithms, evaluating projects on the basis of uncertain long-term benefits introduces additional complexities. We propose comparison rules based on Quicksort and the Bradley--Terry model, which connects rankings to pairwise "win" probabilities. In our model, each agent determines win probabilities of a pair of projects based on his or her specific evaluation of the projects' long-term benefit. The win probabilities are then appropriately aggregated and used to rank projects. Several of the methods we propose perform better than the two most effective aggregation methods currently available. Additionally, our methods can be combined with sampling techniques to significantly reduce the number of pairwise comparisons. We also discuss how the Bradley--Terry portfolio selection approach can be implemented in practice.

Prior spending shutoff experiments in search advertising have found that paid ads cannibalize organic traffic. But it is unclear whether the same is true for other high volume advertising channels like mobile display advertising. We therefore analyzed a large-scale spending shutoff experiment by a US-based mobile game developer, GameSpace. Contrary to previous findings, we found that paid advertising boosts organic installs rather than cannibalizing them. Specifically, every $100 spent on ads is associated with 37 paid and 3 organic installs. The complementarity between paid ads and organic installs is corroborated by evidence of temporal and cross-platform spillover effects: ad spending today is associated with additional paid and organic installs tomorrow and impressions on one platform lead to clicks on other platforms. Our findings demonstrate that mobile app install advertising is about 7.5% more effective than indicated by paid install metrics alone due to spillover effects, suggesting that mobile app developers are under-investing in marketing.

We present a robust Deep Hedging framework for the pricing and hedging of option portfolios that significantly improves training efficiency and model robustness. In particular, we propose a neural model for training model embeddings which utilizes the paths of several advanced equity option models with stochastic volatility in order to learn the relationships that exist between hedging strategies. A key advantage of the proposed method is its ability to rapidly and reliably adapt to new market regimes through the recalibration of a low-dimensional embedding vector, rather than retraining the entire network. Moreover, we examine the observed Profit and Loss distributions on the parameter space of the models used to learn the embeddings. The results show that the proposed framework works well with data generated by complex models and can serve as a construction basis for an efficient and robust simulation tool for the systematic development of an entirely model-independent hedging strategy.

In the context of adapting to global changes, the diversification of the tourist offer seems to be a solution for the mid-mountain areas, which are structured around and dependent on ski tourism. However, it remains unclear how tourism diversification occurs, what forms it can take and what it produces at a territorial scale. In this study, we apply a theory of regional diversification to the case of tourism in order to examine tourism diversification paths. We base our analysis on qualitative data collected on two French study areas: the intercommunities of the massif du Sancy and of the Haut-Chablais. Our results show a pattern in tourism diversification paths, following three steps that can lead to the abandonment of the perimeter of the ski resort. However, among the different types of tourism diversification trajectories, only a saltation form of tourism diversification can lead to the establishment of a larger and more diversified tourism system. Our findings also show that several types of tourism diversification paths can coexist at a territorial scale.

Concentrated liquidity automated market makers (AMMs), such as Uniswap v3, enable liquidity providers (LPs) to earn liquidity rewards by depositing tokens into liquidity pools. However, LPs often face significant financial losses driven by poorly selected liquidity provision intervals and high costs associated with frequent liquidity reallocation. To support LPs in achieving more profitable liquidity concentration, we developed a tractable stochastic optimization problem that can be used to compute optimal liquidity provision intervals for profitable liquidity provision. The developed problem accounts for the relationships between liquidity rewards, divergence loss, and reallocation costs. By formalizing optimal liquidity provision as a tractable stochastic optimization problem, we support a better understanding of the relationship between liquidity rewards, divergence loss, and reallocation costs. Moreover, the stochastic optimization problem offers a foundation for more profitable liquidity concentration.

Multilateral index numbers, such as those used to make international comparisons of prices and income, are fundamental objects in economics. However, these numbers are often challenging to interpret in terms of economic welfare as a data-dependent 'taste bias' can arise for these indices that distorts measurement of price and income levels and dispersion. To study this problem, I develop a means to appraise indices' economic interpretability using non-parametric bounds on a true cost-of-living index. These bounds improve upon their classical counterparts, define a new class of indices, and can correct existing indices for preference misspecification. In my main application I apprise existing international comparison methods. I find that taste bias generally leads to overestimates (underestimates) of price (income) levels. Superlative indices, such as the Fisher-GEKS index, lie within the permitted bounds more frequently than non-superlative methods, but the mean size of this bias is modest in all examined cases. My results can thus be interpreted as supporting the economic validity of the myriad multilateral methods which are in practical use.

We present an architecture for managing Collective Defined Contribution (CDC) schemes. The current approach to UK CDC can be described as shared-indexation, where the nominal benefit of every member in a scheme receives the same level of indexation each year. The design of such schemes rely on the use of approximate discounting methodologies to value liabilities, and this leads to intergenerational cross-subsidies which can be large and unpredictable. We present an alternative approach which we call Collective-Drawdown CDC. This approach does not result in intergenerational cross-subsidies since all pooling is performed by explicit insurance contracts. It is therefore completely fair. Moreover, this scheme results in better pension outcomes when compared to shared-indexation CDC under the same model parameters.

We provide an extension of the unbiased simulation method for SDEs developed in Henry-Labordere et al. [Ann Appl Probab. 27:6 (2017) 1-37] to a class of path-dependent dynamics, pertaining for Asian options. In our setting, both the payoff and the SDE's coefficients depend on the (weighted) average of the process or, more precisely, on the integral of the solution to the SDE against a continuous function with bounded variations. In particular, this applies to the numerical resolution of the class of path-dependent PDEs whose regularity, in the sens of Dupire, is studied in Bouchard and Tan [Ann. I.H.P., to appear].

We propose and implement modern computational methods to enhance catastrophe excess-of-loss reinsurance contracts in practice. The underlying optimization problem involves attachment points, limits, and reinstatement clauses, and the objective is to maximize the expected profit while considering risk measures and regulatory constraints. We study the problem formulation, paving the way for practitioners, for two very different approaches: A local search optimizer using simulated annealing, which handles realistic constraints, and a branch & bound approach exploring the potential of a future speedup via quantum branch & bound. On the one hand, local search effectively generates contract structures within several constraints, proving useful for complex treaties that have multiple local optima. On the other hand, although our branch & bound formulation only confirms that solving the full problem with a future quantum computer would require a stronger, less expensive bound and substantial hardware improvements, we believe that the designed application-specific bound is sufficiently strong to serve as a basis for further works. Concisely, we provide insurance practitioners with a robust numerical framework for contract optimization that handles realistic constraints today, as well as an outlook and initial steps towards an approach which could leverage quantum computers in the future.

In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to adapt to the complexity of the current market dynamics. To overcome these limitations, we propose a hybrid framework for Value-at-Risk (VaR) estimation, combining GARCH volatility models with deep reinforcement learning. Our approach incorporates directional market forecasting using the Double Deep Q-Network (DDQN) model, treating the task as an imbalanced classification problem. This architecture enables the dynamic adjustment of risk-level forecasts according to market conditions. Empirical validation on daily Eurostoxx 50 data covering periods of crisis and high volatility shows a significant improvement in the accuracy of VaR estimates, as well as a reduction in the number of breaches and also in capital requirements, while respecting regulatory risk thresholds. The ability of the model to adjust risk levels in real time reinforces its relevance to modern and proactive risk management.