Price Bounds

Bruce C. Dieffenbach ()
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Bruce C. Dieffenbach: Independent author

Chapter 61 in Conjugate Duality in Economic Analysis, 2026, pp 473-478 from Springer

Abstract: Abstract The fundamental theorem of finance asserts that there is no arbitrage if and only if there exists a positive stochastic discount factor. As a corollary, one obtains upper and lower price bounds for an asset having an arbitrary payoff. Given asset payoffs and prices not allowing any arbitrage, there exists a non-empty set of positive stochastic discount factors. For an extra asset having an arbitrary payoff, to rule out arbitrage its price must be the value of the payoff discounted by one of the positive stochastic discount factors. The supremum of these prices sets an upper bound for the price, and the infimum of these prices sets a lower bound. Interpreting the bounds, the “upper-hedging” and “lower-hedging” duals furnish alternative expressions for the bounds. The upper bound is the minimum price among all larger payoffs in the payoff space, whereas the lower bound is the maximum price among smaller payoffs.

Date: 2026
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DOI: 10.1007/978-3-032-21396-9_61

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