Good–deal bounds
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
- ↑ Jaschke, Stefan; Kuchler, Uwe (2000). "Coherent Risk Measures, Valuation Bounds, and ()-Portfolio Optimization".
- 1 2 3 John R. Birge (2008). Financial Engineering. Elsevier. pp. 521–524. ISBN 978-0-444-51781-4.
- ↑ Arai, Takuji; Fukasawa, Masaaki (2011). "Convex risk measures for good deal bounds" (pdf). Retrieved October 14, 2011.