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          Quantitative Finance

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          New submissions for Mon, 27 Apr 20

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          Error with 2004.11686
          Error with 2004.11697
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          Cross-lists for Mon, 27 Apr 20

          [5]  arXiv:1506.07368 (cross-list from q-fin.EC) [pdf, other]
          Title: On Game-Theoretic Risk Management (Part One) - Towards a Theory of Games with Payoffs that are Probability-Distributions
          Authors: Stefan Rass
          Subjects: General Economics (econ.GN); Statistics Theory (math.ST); Applications (stat.AP)

          Optimal behavior in (competitive) situation is traditionally determined with the help of utility functions that measure the payoff of different actions. Given an ordering on the space of revenues (payoffs), the classical axiomatic approach of von Neumann and Morgenstern establishes the existence of suitable utility functions, and yields to game-theory as the most prominent materialization of a theory to determine optimal behavior. Although this appears to be a most natural approach to risk management too, applications in critical infrastructures often violate the implicit assumption of actions leading to deterministic consequences. In that sense, the gameplay in a critical infrastructure risk control competition is intrinsically random in the sense of actions having uncertain consequences. Mathematically, this takes us to utility functions that are probability-distribution-valued, in which case we loose the canonic (in fact every possible) ordering on the space of payoffs, and the original techniques of von Neumann and Morgenstern no longer apply.
          This work introduces a new kind of game in which uncertainty applies to the payoff functions rather than the player's actions (a setting that has been widely studied in the literature, yielding to celebrated notions like the trembling hands equilibrium or the purification theorem). In detail, we show how to fix the non-existence of a (canonic) ordering on the space of probability distributions by only mildly restricting the full set to a subset that can be totally ordered. Our vehicle to define the ordering and establish basic game-theory is non-standard analysis and hyperreal numbers.

          Error with 2004.11485

          Replacements for Mon, 27 Apr 20

          [7]  arXiv:1506.07368 (replaced) [pdf, other]
          Title: On Game-Theoretic Risk Management (Part One) - Towards a Theory of Games with Payoffs that are Probability-Distributions
          Authors: Stefan Rass
          Subjects: General Economics (econ.GN); Statistics Theory (math.ST); Applications (stat.AP)
          [8]  arXiv:1807.11477 (replaced) [pdf, other]
          Title: Explaining Parochialism: A Causal Account for Political Polarization in Changing Economic Environments
          Subjects: General Economics (econ.GN); Physics and Society (physics.soc-ph); Populations and Evolution (q-bio.PE)
          [9]  arXiv:2002.07561 (replaced) [pdf, other]
          Title: The Market Price of Risk for Delivery Periods: Pricing Swaps and Options in Electricity Markets
          Subjects: Pricing of Securities (q-fin.PR); Mathematical Finance (q-fin.MF)
          [10]  arXiv:2002.09037 (replaced) [pdf]
          Title: Sustainability and fairness simulations based on decision-making model of utility function and norm function
          Comments: 30 pages, 12 figures. arXiv admin note: text overlap with arXiv:2002.09036
          Subjects: General Economics (econ.GN)
          [11]  arXiv:2003.11352 (replaced) [pdf, other]
          Title: Cryptocurrency Trading: A Comprehensive Survey
          Subjects: Trading and Market Microstructure (q-fin.TR); Computational Finance (q-fin.CP)
          [ total of 11 entries: 1-11 ]
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