arXiv subjects

Lorenzo Bastianello

Publications and source records attributed to Lorenzo Bastianello.

8 recordsLinked to original sources

arXiv2026

Future-blindness and the product topology

We study future-blind preferences, which are preferences that heavily discount the future, within the space of infinite consumption streams. We give two definitions: $N$-blindness, where agents ignore periods beyond a fixed date $N$, and eventual blindness, where all but finitely many dates are neglected. Using a topological approach, we show that the finest topology ensuring eventual blindness coincides with the product topology. This provides a behavioral foundation for continuity in the product topology, which was considered for studying equilibrium existence in infinite-dimensional spaces. Finally, we characterize the dual spaces under these topologies.

econ.TH↗

arXiv2024

Discounted Subjective Expected Utility in Continuous Time

By embedding uncertainty into time, we obtain a conjoint axiomatic characterization of both Exponential Discounting and Subjective Expected Utility that accommodates arbitrary state and outcome spaces. In doing so, we provide a novel and simple time-interpretation of subjective probability. The subjective probability of an event is calibrated using time discounting.

econ.TH↗

arXiv2023

Rationality and correctness in n-player games

There are two well-known sufficient conditions for Nash equilibrium in two-player games: mutual knowledge of rationality (MKR) and mutual knowledge of conjectures. MKR assumes that the concept of rationality is mutually known. In contrast, mutual knowledge of conjectures assumes that a given profile of conjectures is mutually known, which has long been recognized as a strong assumption. In this note, we introduce a notion of "mutual assumption of rationality and correctness" (MARC), which conceptually aligns more closely with the MKR assumption. We present two main results. Our first result establishes that MARC holds in every two-person zero-sum game. In our second theorem, we show that MARC does not in general hold in n-player games.

econ.TH↗

arXiv2023

Gain-Loss Hedging and Cumulative Prospect Theory

Two acts are comonotonic if they yield high payoffs in the same states of nature. The main purpose of this paper is to derive a new characterization of Cumulative Prospect Theory (CPT) through simple properties involving comonotonicity. The main novelty is a concept dubbed gain-loss hedging: mixing positive and negative acts creates hedging possibilities even when acts are comonotonic. This allows us to clarify in which sense CPT differs from Choquet expected utility. Our analysis is performed under the simpler case of (piece-wise) constant marginal utility which allows us to clearly separate the perception of uncertainty from the evaluation of outcomes.

econ.TH↗

arXiv2022

Conditional strategy equilibrium

In this note, we prove the existence of an equilibrium concept, dubbed conditional strategy equilibrium, for non-cooperative games in which a strategy of a player is a function from the other players' actions to her own actions. We study the properties of efficiency and coalition-proofness of the conditional strategy equilibrium in $n$-person games.

econ.TH↗

arXiv2022

Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules

If prices of assets traded in a financial market are determined by non-linear pricing rules, different versions of the Call-Put Parity have been considered. We show that, under monotonicity, parities between call and put options and discount certificates characterize ambiguity-sensitive (Choquet and/or Sipos) pricing rules, i.e., pricing rules that can be represented via discounted expectations with respect to non-additive probability measures. We analyze how non-additivity relates to arbitrage opportunities and we give necessary and sufficient conditions for Choquet and Sipos pricing rules to be arbitrage-free. Finally, we identify violations of the Call-Put Parity with the presence of bid-ask spreads.

econ.TH↗

arXiv2020

Dynamically Consistent Objective and Subjective Rationality

A group of experts, for instance climate scientists, is to choose among two policies $f$ and $g$. Consider the following decision rule. If all experts agree that the expected utility of $f$ is higher than the expected utility of $g$, the unanimity rule applies, and $f$ is chosen. Otherwise the precautionary principle is implemented and the policy yielding the highest minimal expected utility is chosen. This decision rule may lead to time inconsistencies when an intermediate period of partial resolution of uncertainty is added. We provide axioms that enlarge the initial group of experts with veto power, which leads to a set of probabilistic beliefs that is "rectangular" in a minimal sense. This makes this decision rule dynamically consistent and provides, as a byproduct, a novel behavioral characterization of rectangularity.

econ.TH↗

arXiv2020

Time discounting under uncertainty

We study intertemporal decision making under uncertainty. We fully characterize discounted expected utility in a framework à la Savage. Despite the popularity of this model, no characterization is available in this setting. The concept of stationarity, introduced by Koopmans for deterministic discounted utility, plays a central role for both attitudes towards time and towards uncertainty. We show that a strong stationarity axiom characterizes discounted expected utility. When hedging considerations are taken into account, a weaker stationarity axiom generalizes discounted expected utility to Choquet discounted expected utility, allowing for non-neutral attitudes towards uncertainty.

econ.TH↗