arXiv subjects

Massimo Marinacci

Publications and source records attributed to Massimo Marinacci.

14 recordsLinked to original sources

arXiv2026

Nonconcave Portfolio Choice under Smooth Ambiguity

We study continuous-time portfolio choice with nonlinear payoffs under smooth ambiguity and Bayesian learning. We develop a general framework for dynamic, non-concave asset allocation that accommodates nonlinear payoffs, broad utility classes, and flexible ambiguity attitudes. Dynamic consistency is obtained by a robust representation that recasts the ambiguity-averse problem as ambiguity-neutral with distorted priors. This structure delivers explicit trading rules by combining nonlinear filtering with the martingale approach and nests standard concave and linear-payoff benchmarks. As a leading application, delegated management with convex incentives illustrates that ambiguity aversion shifts beliefs toward adverse states, limits the range of states that would otherwise trigger more aggressive risk taking, and reduces volatility through lower risky exposure.

q-fin.PM↗

arXiv2024

Affine Gateaux Differentials and the von Mises Statistical Calculus

This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear functionals typically employed in standard Gateaux differentiability. This affine notion of differentiability naturally arises in certain applications and has been utilized by some authors in the statistics literature. We aim to offer a unified and comprehensive perspective on this concept.

math.FA↗

arXiv2023

Risk Aversion and Insurance Propensity

We provide a new foundation of risk aversion by showing that this attitude is fully captured by the propensity to seize insurance opportunities. Our foundation, which applies to all probabilistically sophisticated preferences, well accords with the commonly held prudential interpretation of risk aversion that dates back to the seminal works of Arrow (1963) and Pratt (1964). In our main results, we first characterize the Arrow-Pratt risk aversion in terms of propensity to full insurance and the stronger notion of risk aversion of Rothschild and Stiglitz (1970) in terms of propensity to partial insurance. We then extend the analysis to comparative risk aversion by showing that the notion of Yaari (1969) corresponds to comparative propensity to full insurance, while the stronger notion of Ross (1981) corresponds to comparative propensity to partial insurance.

econ.TH↗

arXiv2023

Capacities and Choquet Averages of Ultrafilters

We show that a normalized capacity $\nu: \mathcal{P}(\mathbf{N})\to \mathbf{R}$ is invariant with respect to an ideal $\mathcal{I}$ on $\mathbf{N}$ if and only if it can be represented as a Choquet average of $\{0,1\}$-valued finitely additive probability measures corresponding to the ultrafilters containing the dual filter of $\mathcal{I}$. This is obtained as a consequence of an abstract analogue in the context of Archimedean Riesz spaces.

math.FA↗

arXiv2023

Algorithmic Decision Processes

We develop a full-fledged analysis of an algorithmic decision process that, in a multialternative choice problem, produces computable choice probabilities and expected decision times.

econ.TH↗

arXiv2023

Recursive Preferences and Ambiguity Attitudes

Monotonicity and recursivity are central assumptions in intertemporal consumption problems under ambiguity. We show that monotone recursive preferences admit both a recursive and an ex-ante representation, and that the certainty equivalent functionals associated with these representations are translation invariant. Translation invariance implies that the decision maker's ambiguity attitudes are constant, in the sense that they do not vary with the level of welfare or utility. Finally, we establish an equation linking the two certainty equivalent functionals that extends the notion of rectangularity for recursive multiple priors, which we call generalized rectangularity. This equation yields a simple, testable condition for dynamic consistency.

econ.TH↗

arXiv2020

Ergodic Annealing

Simulated Annealing is the crowning glory of Markov Chain Monte Carlo Methods for the solution of NP-hard optimization problems in which the cost function is known. Here, by replacing the Metropolis engine of Simulated Annealing with a reinforcement learning variation -- that we call Macau Algorithm -- we show that the Simulated Annealing heuristic can be very effective also when the cost function is unknown and has to be learned by an artificial agent.

cs.AI↗

arXiv2020

Making Decisions under Model Misspecification

We use decision theory to confront uncertainty that is sufficiently broad to incorporate "models as approximations." We presume the existence of a featured collection of what we call "structured models" that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max-min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns.

econ.TH↗

arXiv2020

A Canon of Probabilistic Rationality

We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, thus it consists of alternatives that are optimal according to some preference, and random choice then occurs according to a tie breaking among such alternatives that satisfies Renyi's Conditioning Axiom. Our result shows that the Choice Axiom is, in a precise formal sense, a probabilistic version of the Weak Axiom. It thus supports Luce's view of his own axiom as a "canon of probabilistic rationality."

econ.TH↗

arXiv2020

Axiomatic Tests for the Boltzmann Distribution

The Boltzmann distribution describes a single parameter (temperature) family of probability distributions over a state space; at any given temperature, the ratio of probabilities of two states depends on their difference in energy. The same family is known in other disciplines (economics, psychology, computer science) with different names and interpretations. Such widespread use in very diverse fields suggests a common conceptual structure. We identify it on the basis of few natural axioms. Checking whether observables satisfy these axioms is easy, so our characterization provides a simple empirical test of the Boltzmannian modeling theories.

math.PR↗

arXiv2020

Multialternative Neural Decision Processes

We introduce an algorithmic decision process for multialternative choice that combines binary comparisons and Markovian exploration. We show that a preferential property, transitivity, makes it testable.

cs.AI↗

arXiv2020

Multinomial logit processes and preference discovery: inside and outside the black box

We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation \[ p_{t}\left( a,A\right) =\dfrac{e^{\frac{u\left( a\right) }{\lambda \left( t\right) }+\alpha \left( a\right) }}{\sum_{b\in A}e^{\frac{u\left( b\right) }{\lambda \left( t\right) }+\alpha \left( b\right) }}% \] where $p_{t}\left( a,A\right) $ is the probability that alternative $a$ is selected from the set $A$ of feasible alternatives if $t$ is the time available to decide, $\lambda$ is a time dependent noise parameter measuring the unit cost of information, $u$ is a time independent utility function, and $\alpha$ is an alternative-specific bias that determines the initial choice probabilities reflecting prior information and memory anchoring. Our axiomatic analysis provides a behavioral foundation of softmax (also known as Multinomial Logit Model when $\alpha$ is constant). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behavior. Jointly, the two approaches provide a thorough understanding of soft-maximization in terms of internal causes (neurophysiological mechanisms) and external effects (testable implications).

econ.TH↗

arXiv2015

Ergodic Theorems for Lower Probabilities

We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As a by-product, we provide a version for lower probabilities of the Strong Law of Large Numbers.

math.FA↗

arXiv2005

A strong law of large numbers for capacities

We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.

math.PR↗