arXiv subjects

Peter P. Wakker

Publications and source records attributed to Peter P. Wakker.

2 recordsLinked to original sources

arXiv2024

Anticomonotonicity for Preference Axioms: The Natural Counterpart to Comonotonicity

Comonotonicity (``same variation'') of random variables minimizes hedging possibilities and has been widely used, e.g., in Gilboa and Schmeidler's ambiguity models. This paper investigates anticomonotonicity (``opposite variation''; abbreviated ``AC''), the natural counterpart to comonotonicity. It minimizes leveraging rather than hedging possibilities. Surprisingly, AC restrictions of several traditional axioms do not give new models. Instead, they strengthen the foundations of existing classical models: (a) linear functionals through Cauchy's equation; (b) Anscombe-Aumann expected utility; (c) as-if-risk-neutral pricing through no-arbitrage; (d) de Finetti's bookmaking foundation of Bayesianism using subjective probabilities; (e) risk aversion in Savage's subjective expected utility. In each case, our generalizations show where the critical tests of classical axioms lie: in the AC cases (maximal hedges). We next present examples where AC restrictions do essentially weaken existing axioms, and do provide new properties and new models.

econ.TH↗

arXiv2012

Decision Principles to justify Carnap's Updating Method and to Suggest Corrections of Probability Judgments (Invited Talks)

This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s classical result, AND can therefore be applied TO ANY finite Bayesian network.It neither requires linear utility AS did de Finetti s classical result, AND r ntherefore allows FOR the empirically AND normatively desirable risk r naversion.Finally, BY identifying AND fixing utility IN an elementary r nmanner, our result can readily be applied TO identify methods OF r nprobability updating.Thus, a decision - theoretic foundation IS given r nto the computationally efficient method OF inductive reasoning r ndeveloped BY Rudolf Carnap.Finally, recent empirical findings ON r nprobability assessments are discussed.It leads TO suggestions FOR r ncorrecting biases IN probability assessments, AND FOR an alternative r nto the Dempster - Shafer belief functions that avoids the reduction TO r ndegeneracy after multiple updatings.r n

cs.AI↗