Measures of model uncertainty and calibrated option bounds

References

• Artzner , P , Delbaen , F , Eber , JM and Heath , D . 1999 . Coherent measures of risk . Math. Finance , 9 ( 3 ) : 203 – 228 .
   Web of Science ®Google Scholar
• Avellanedas , M , Levy , A and Parás , P . 1995 . Pricing and hedging derivative securities in markets with uncertain volatilities . Appl. Math. Finance , 2 ( 2 ) : 73 – 89 .
   Google Scholar
• Avellanedas , M and Parás , P . 1996 . Managing the volatility risk of portfolios of derivative securities: The Lagrangian uncertainty model . Appl. Math. Finance , 3 ( 1 ) : 21 – 52 .
   Google Scholar
• Björk , T . 1998 . Arbitrage Theory in Continuous Time , 1st , Oxford : Oxford University Press .
   Google Scholar
• Brooke , A , Kendrick , D and Meeraus , A . 1992 . GAMS: A User's Guide , San Fransisco, CA : The Scientific Press .
   Google Scholar
• Cont , R . 2006 . Model Uncertainty and its impact on the pricing of derivative instruments . Math. Finance , 16 ( 3 ) : 519 – 547 .
   Web of Science ®Google Scholar
• 2007 . CPLEX 10.0 Solver Manual , ILOG . http://www.gans.com/dd/docs/solvers/cplex.pdf
   Google Scholar
• Drud , A . 2007 . CONOPT Solver Manual, ARKI Consulting , Denmark : Bagsvaerd . http://www.gans.com/dd/docs/solvers/conopt.pdf
   Google Scholar
• Edirisinghe , NCP , Naik , V and Uppal , R . 1993 . Optimal replication of options with transaction costs and trading restrictions . J. Financ. Quant. Anal. , 28 : 117 – 138 .
   Web of Science ®Google Scholar
• Epstein , LG . 1999 . A definition of uncertainty aversion . Rev. Econ. Stud. , 65 : 579 – 608 .
   Google Scholar
• Epstein , LG and Wang , L . 1995 . Uncertainty, risk neutral measures, and asset price booms and crashes . J. Econ. Theory , 67 : 40 – 80 .
   Google Scholar
• Föllmer , H and Schied , A . 2002 . Convex measures of risk and trading constraints . Finance Stoch. , 6 ( 4 ) : 429 – 447 .
   Web of Science ®Google Scholar
• Föllmer , H and Schied , A . 2002 . Stochastic Finance: An Introduction in Discrete Time , Vol. 27 , De Gruyter, Berlin : De Gruyter Studies in Mathematics .
   Google Scholar
• Gilboa , I and Schmeidler , D . 1989 . Maxmin expected utility with non-unique prior . J. Math. Econ. , 18 : 141 – 153 .
   Web of Science ®Google Scholar
• Jackwerth , JC . 1999 . Option-implied risk-neutral distributions and implied binomial trees; a literature review . J. Deriv. , 7 ( 2 ) : 66 – 82 .
   Google Scholar
• King , AJ . 2002 . Duality and Martingales: A stochastic programming perspective on contingent claims . Math. Program. Ser. B , 91 : 543 – 562 .
   Web of Science ®Google Scholar
• King , AJ , Koivu , M and Pennanen , T . 2005 . Calibrated option bounds . Int. J. Theor. Appl. Finance , 8 ( 2 ) : 141 – 159 .
   Google Scholar
• Knight , F . 1921 . Risk, Uncertainty and Profit , Boston, MA : Houghton Mifflin .
   Google Scholar
• Omberg , E . 1988 . Efficient discrete time jump process models in option pricing . J. Financ. Quant. Anal. , 23 ( 2 ) : 161 – 174 .
   Web of Science ®Google Scholar
• Pennanen , T and Koivu , M . 2002 . Integration quadratures in discretization of stochastic programs , stochastic programming E-Print Series . http://edoc.hu-berlin.de/docviews/abstract.php?lang=ger&id=26680
   Google Scholar
• Pliska , SR . 1997 . Introduction to Mathematical Finance: Discrete Time Models , Malden, MA : Blackwell Publishers .
   Google Scholar
• Rockafellar , RT . 1970 . Convex Analysis , Princeton, NJ : Princeton University Press .
   Google Scholar
• Routledge , BR and Zin , S . 2001 . Model uncertainty and liquidity , NBER Working Paper 8683 http://ssrn.com/abstract=294732
   Google Scholar
• Schied , A . 2006 . Risk measures and robust optimization problems . Stoch. Models , 22 ( 4 ) : 753 – 831 .
   Web of Science ®Google Scholar
• Schied , A and Wu , C-T . 2005 . Duality theory for optimal investments under model uncertainty . Stat. Decisions , 23 ( 3 ) : 199 – 217 .
   Google Scholar
• Stockbridge , RH . Option pricing for finite models with limits on hedging . The 4th Asian control conference . September 2002 . pp. 1563 – 1568 . Singapore 2002
   Google Scholar