Gain-loss pricing under ambiguity of measure
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 16, Issue: 1, page 132-147
- ISSN: 1292-8119
Access Full Article
topAbstract
topHow to cite
topReferences
top- A. Ben-Tal and A. Nemirovski, Optimization I-II, Convex Analysis, Nonlinear Programming, Nonlinear Programming Algorithms, Lecture Notes. Technion, Israel Institute of Technology (2004), available for download at nemirovs/Lect_OptI-II.pdf. URIhttp://www2.isye.gatech.edu/
- A. Ben-Tal and M. Teboulle, An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance17 (2007) 449–476.
- A.E. Bernardo and O. Ledoit, Gain, loss and asset pricing. J. Political Economy81 (2000) 637–654.
- D. Bertsimas and I. Popescu, On the relation between option and stock prices: An optimization approach. Oper. Res.50 (2002) 358–374.
- D. Bertsimas and I. Popescu, Optimal inequalities in probability theory: A convex optimization approach. SIAM J. Optim.15 (2005) 780–804.
- F. Black and M. Scholes, The pricing of options and corporate liabilities. J. Political Economy108 (1973) 144–172.
- A. Brooke, D. Kendrick and A. Meeraus, GAMS: A User's Guide. The Scientific Press, San Fransisco, California (1992).
- G. Calafiore, Ambiguous risk measures and optimal robust portfolios. SIAM J. Optim.18 (2007) 853–877.
- R. Cont, Model uncertainty and its impact on the pricing of derivative instruments. Math. Finance16 (2006) 519–547.
- I. Csiszar, Information-type measures of difference of probability distributions and indirect observations. Studia Sci. Math. Hungarica2 (1967) 299–318.
- A. d'Aspremont and L. El Ghaoui, Static arbitrage bounds on basket option prices. Math. Programming106 (2006) 467–489.
- A. Eichhorn and W. Römisch, Polyhedral risk measures in stochastic programming. SIAM J. Optim.16 (2005) 69–95.
- L. El Ghaoui, M. Oks and F. Oustry, Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res.51 (2003) 543–556.
- L.G. Epstein, A definition of uncertainty aversion. Rev. Economic Studies65 (1999) 579–608.
- M.C. Ferris and T.S. Munson, Interfaces to PATH 3.0: Design, implementation and usage. Technical Report, University of Wisconsin, Madison (1998).
- H. Föllmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time, De Gruyter Studies in Mathematics27. Second Edition, Berlin (2004).
- J.M. Harrison and D.M. Kreps, Martingales and arbitrage in multiperiod securities markets. J. Economic Theory20 (1979) 381–408.
- J.M. Harrison and S.R. Pliska, Martingales and stochastic integrals in the theory of continuous trading. Stoch. Process. Appl.11 (1981) 215–260.
- A.J. King and L.A. Korf, Martingale Pricing Measures in Incomplete Markets via Stochastic Programming Duality in the Dual of . Technical Report (2001).
- L.A. Korf, Stochastic programming duality: multipliers for unbounded constraints with an application to mathematical finance. Math. Programming99 (2004) 241–259.
- S. Kullback, Information Theory and Statistics. Wiley, New York (1959)
- H.J. Landau, Moments in mathematics, in Proc. Sympos. Appl. Math.37, H.J. Landau Ed., AMS, Providence, RI (1987).
- I.R. Longarela, A simple linear programming approach to gain, loss and asset pricing. Topics in Theoretical Economics2 (2002) Article 4.
- T.R. Rockafellar, Conjugate Duality and Optimization. SIAM, Philadelphia (1974).
- A. Ruszczyński and A. Shapiro, Optimization of risk measures, in Probabilistic and Randomized Methods for Design under Uncertainty, G. Calafiore and F. Dabbene Eds., Springer, London (2005).
- A. Ruszczyński and A. Shapiro, Optimization of convex risk functions. Math. Oper. Res.31 (2006) 433–452.
- A. Shapiro, On duality theory of convex semi-infinite programming. Optimization54 (2005) 535–543.
- A. Shapiro and S. Ahmed, On a class of stochastic minimax programs. SIAM J. Optim.14 (2004) 1237–1249.
- A. Shapiro and A. Kleywegt, Minimax analysis of stochastic problems. Optim. Methods Software17 (2002) 523–542.
- J.E. Smith, Generalized Chebychev inequalities: Theory and applications in decision analysis. Oper. Res.43 (1995) 807–825.
- Sh. Tian and R.J.-B. Wets, Pricing Contingent Claims: A Computational Compatible Approach. Technical Report, Department of Mathematics, University of California, Davis (2006).