Quantitative Finance

Dreyfuss, Bnaya; Raux, Raphaël

doi: 10.48550/arxiv.2406.05408pmid: N/A

Abstract:We study \emph{Human Projection} (HP): people's tendency to evaluate AI using the same frameworks they use for humans -- treating features such as task difficulty and the reasonableness of mistakes as diagnostic of overall ability. We formalize HP and its consequences for equilibrium adoption, testing its predictions experimentally. First, people project human difficulty onto AI, overestimating performance on human-easy tasks, underestimating it on human-hard ones, and over-updating after easy failures and hard successes -- leading to systematic misspecification when AI performance is jagged rather than human-ordered. Second, HP interprets observed performance through a single ability index, inducing all-or-nothing adoption even when AI outperforms humans on only some tasks; experimentally stripping AI of human-like cues weakens cross-task generalization and reduces over-adoption. Finally, a field experiment with a parenting-advice chatbot shows that less humanly reasonable mistakes cause larger drops in trust and future engagement. Anthropomorphic AI design can amplify HP, misaligning beliefs and distorting adoption.

Mariani, Francesca; Recchioni, Maria Cristina; Wang, Tai-Ho; Giacalone, Roberto

doi: 10.48550/arxiv.2406.05854pmid: N/A

Abstract:An empirical analysis, suggested by optimal Merton dynamics, reveals some unexpected features of asset volumes. These features are connected to traders' belief and risk aversion. This paper proposes a trading strategy model in the optimal Merton framework that is representative of the collective behavior of heterogeneous rational traders. This model allows for the estimation of the average risk aversion of traders acting on a specific risky asset, while revealing the existence of a price of risk closely related to market price of risk and volume rate. The empirical analysis, conducted on real data, confirms the validity of the proposed model.

Amendola, Alessandra; Candila, Vincenzo; Naimoli, Antonio; Storti, Giuseppe

doi: 10.48550/arxiv.2406.06235pmid: N/A

Abstract:To comply with increasingly stringent international standards in risk management and regulation, several approaches have been developed in the literature for forecasting tail-risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). However, the accuracy of these measures can be significantly affected by multiple sources of uncertainty, including model misspecification, data limitations and estimation procedures. To address these challenges and enhance the predictive performance of individual models, this study introduces novel forecast combination strategies based on the Model Confidence Set (MCS) methodology. Specifically, a strictly consistent joint VaR-ES loss function is employed to identify the best-performing models, which constitute the Set of Superior Models (SSM). Subsequently, the VaR and ES forecasts of the models included in the SSM are combined using various weighting schemes. An empirical analysis based on nine stock market indices at the 2.5\% and 1\% risk levels provides evidence that the proposed combined predictors are a robust alternative for forecasting tail-risk measures, successfully passing standard backtests and consistently entering the SSM of the MCS.

Angoshtari, Bahman; Yu, Xiang; Yuan, Fengyi

doi: 10.48550/arxiv.2406.20063pmid: N/A

Abstract:This paper studies a loss-averse version of the multiplicative habit formation preference and the corresponding optimal investment and consumption strategies over an infinite horizon. The agent's consumption preference is depicted by a general S-shaped utility function of her consumption-to-habit ratio. By considering the concave envelope of the S-shaped utility and the associated dual value function, we provide a thorough analysis of the HJB equation for the concavified problem via studying a related nonlinear free boundary problem. Based on established properties of the solution to this free boundary problem, we obtain the optimal consumption and investment policies in feedback form. Some new and technical verification arguments are developed to cope with generality of the utility function. The equivalence between the original problem and the concavified problem readily follows from the structure of the feedback controls. We also discuss some quantitative properties of the optimal policies, complemented by illustrative numerical examples and their financial implications.