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He was the author of 26 books, including his investment best-seller, The Zurich Axioms. Born in England , Gunther moved to the United States aged 11 after his father, Franz Heinrich (Frank Henry) became the manager of the New York branch of a leading Swiss bank, Schweizerischer Bankverein ( Swiss Bank Corporation or SBC ).
That is, if portfolio always has better values than portfolio under almost all scenarios then the risk of should be less than the risk of . [2] E.g. If is an in the money call option (or otherwise) on a stock, and is also an in the money call option with a lower strike price.
In decision theory, the Ellsberg paradox (or Ellsberg's paradox) is a paradox in which people's decisions are inconsistent with subjective expected utility theory. John Maynard Keynes published a version of the paradox in 1921. [1]
In a discrete (i.e. finite state) market, the following hold: [2] The First Fundamental Theorem of Asset Pricing: A discrete market on a discrete probability space (,,) is arbitrage-free if, and only if, there exists at least one risk neutral probability measure that is equivalent to the original probability measure, P.
The Dutch book arguments are used to explore degrees of certainty in beliefs, and demonstrate that rational agents must be Bayesian; [2] in other words, rationality requires assigning probabilities to events that behave according to the axioms of probability, and having preferences that can be modeled using the von Neumann–Morgenstern axioms.
The key financial insight behind the model is that one can perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk", absenting the risk adjustment from the pricing (, the value, or price, of the option, grows at , the risk-free rate).
In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. The study of non-well-founded sets was initiated by Dmitry Mirimanoff in a series of papers between 1917 and 1920, in which he formulated the distinction between well-founded and non-well-founded sets; he did not regard well-foundedness as ...
The axiom of regularity is of a restrictive nature as well. Therefore, one is led to the formulation of other axioms to guarantee the existence of enough sets to form a set theory. Some of these have been described informally above and many others are possible. Not all conceivable axioms can be combined freely into consistent theories.