arXiv subjects

Benedikt Koch

Publications and source records attributed to Benedikt Koch.

3 recordsLinked to original sources

arXiv2026

An Axiomatic Foundation for Decisions with Counterfactual Utility

Counterfactual utilities evaluate decisions not only by the realized outcome under a given decision, but also by the counterfactual outcomes that would arise under alternative decisions. By generalizing the standard utility framework, they allow decision-makers to encode asymmetric criteria, such as avoiding harm and anticipating regret. Recent work, however, has raised fundamental concerns about the coherence and transitivity of counterfactual utilities. We address these concerns by extending the von Neumann-Morgenstern (vNM) framework to preferences defined on the extended space of all potential outcomes rather than realized outcomes alone. We show that expected counterfactual utility satisfies the vNM axioms on this extended domain, thereby admitting a coherent preference representation. We further examine how counterfactual preferences map onto the realized outcome space through menu-dependent and context-dependent projections. This axiomatic framework reconciles apparent inconsistencies highlighted by the Russian roulette example in the statistics literature and resolves the well-known Allais paradox from behavioral economics. We also derive an additional axiom required to reduce counterfactual utilities to standard utilities on the same potential outcome space, and establish an axiomatic foundation for additive counterfactual utilities, which satisfy a necessary and sufficient condition for point identification. Our results show that the use of asymmetric counterfactual utility functions is coherent regardless of whether individual potential outcomes are deterministic or stochastic, and that a recent proposal involving stochastic potential outcomes leads to ambiguities and inconsistencies.

econ.TH↗

arXiv2025

Ergodic robust maximization of asymptotic growth with stochastic factor processes

We consider a robust asymptotic growth problem under model uncertainty in the presence of stochastic factors. We fix two inputs representing the instantaneous covariance for the asset price process $X$, which depends on an additional stochastic factor process $Y$, as well as the invariant density of $X$ together with $Y$. The stochastic factor process $Y$ has continuous trajectories but is not even required to be a semimartingale. Our setup allows for drift uncertainty in $X$ and model uncertainty for the local dynamics of $Y$. This work builds upon a recent paper of Kardaras & Robertson, where the authors consider an analogous problem, however, without the additional stochastic factor process. Under suitable, quite weak assumptions we are able to characterize the robust optimal trading strategy and the robust optimal growth rate. The optimal strategy is shown to be functionally generated and, remarkably, does not depend on the factor process $Y$. Our result provides a comprehensive answer to a question proposed by Fernholz in 2002. We also show that the optimal strategy remains optimal even in the more restricted case where $Y$ is a semimartingale and the joint covariation structure of $X$ and $Y$ is prescribed as a function of $X$ and $Y$. Our results are obtained using a combination of techniques from partial differential equations, calculus of variations, and generalized Dirichlet forms.

q-fin.MF↗

arXiv2025

Statistical Decision Theory with Counterfactual Loss

Many researchers apply classical statistical decision theory to evaluate treatment choices and learn optimal policies. However, because this framework relies solely on realized outcomes under chosen actions and ignores counterfactuals, it cannot assess the quality of a decision relative to feasible alternatives at the unit level, which is an important requirement in some settings. For example, in pretrial bail decisions, a judge must balance crime prevention upon release against the risk of imposing unnecessary burdens on arrestees. A central challenge in this framework is identification: since only one potential outcome is observed per unit, counterfactual risk is typically not identifiable. We show that, under strong ignorability, counterfactual risk is identifiable if and only if the loss is additive in the potential outcomes. We further demonstrate that additive counterfactual losses can yield treatment recommendations that differ from those based on standard losses when more than two treatment options are available. We show that additive counterfactual losses capture not only decision accuracy but also decision difficulty, whereas standard losses reflect accuracy alone. Finally, we introduce a symbolic linear inverse program that determines whether a given counterfactual loss yields an identifiable risk, without requiring data.

math.ST↗