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Good–deal bounds

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Good–deal bounds are price bounds for a financial portfolio which depends on an individual trader's preferences. Mathematically, if is a set of portfolios with future outcomes which are "acceptable" to the trader, then define the function by

where is the set of final values for self-financing trading strategies. Then any price in the range does not provide a good deal for this trader, and this range is called the "no good-deal price bounds."[1][2]

If then the good-deal price bounds are the no-arbitrage price bounds, and correspond to the subhedging and superhedging prices. The no-arbitrage bounds are the greatest extremes that good-deal bounds can take.[2][3]

If where is a utility function, then the good-deal price bounds correspond to the indifference price bounds.[2]

References

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  1. ^ Jaschke, Stefan; Kuchler, Uwe (2000). "Coherent Risk Measures, Valuation Bounds, and ()-Portfolio Optimization". {{cite journal}}: Cite journal requires |journal= (help)
  2. ^ a b c John R. Birge (2008). Financial Engineering. Elsevier. pp. 521–524. ISBN 978-0-444-51781-4.
  3. ^ Arai, Takuji; Fukasawa, Masaaki (2011). "Convex risk measures for good deal bounds". arXiv:1108.1273v1 [q-fin.PR].