A convex duality approach for pricing contingent claims under partial information and short selling constraints

References

• Anderson, E. J., and Nash, P. 1987. Linear Programming in Infinite Dimensional Spaces: Theory and Applications. Wiley-Interscience Series in Discrete Mathematics and Optimization. Hoboken, NJ: Wiley.
   Google Scholar
• Bouchard, B. 2006. No-arbitrage in discrete-time markets with proportional transaction costs and general Information structure. Finance and Stochastics 10:276–297.
   Web of Science ®Google Scholar
• Cvitanić, J., and Karatzas, I. 1993. Hedging contingent claims with constrained portfolios. Annals of Applied Probability 3:652–681.
   Google Scholar
• De Vallière, D., Kabanov, Y., and Stricker, C. 2007. No-arbitrage criteria for financial markets with transaction costs and incomplete information. Finance and Stochastics 11:237–251.
   Web of Science ®Google Scholar
• Devolder, O., Glineur, F., and Nesterov, Y. 2010. Solving infinite-dimensional optimization problems by polynomial approximation. Discussion Paper. Center for Research and Econometrics, Belgium.
   Google Scholar
• Föllmer, H., and Kramkov, D. 1997. Optional decompositions under constraints. Probability Theory and Related Fields 109:1–25.
   Web of Science ®Google Scholar
• Frittelli, M., and Rozassa Gianin, E. 2002. Putting order in risk measures. Journal of Banking and Finance 26:1473–1486.
   Web of Science ®Google Scholar
• Jouini, E., and Kallal, H. 1995. Arbitrage in securities markets with short-sales constraints. Mathematical Finance 3:197–232.
   Google Scholar
• Kabanov, Y., and Stricker, C. 2006. The Dalang–Morton–Willinger Theorem Under Delayed and Restricted Information. In Memoriam Paul-André Meyer. Berlin: Springer.
   Google Scholar
• Kabanov, Y., Stricker, C., and Yu, M. 2001. A Teacher’s Note on No Arbitrage Criteria. Séminaire de Probabilités XXXV. Lecture Notes on Mathematics 1755. Berlin: Springer, 149–152.
   Google Scholar
• Karatzas, I., and Kou, S. G. 1998. Hedging American contingent claims with constrained portfolios. Finance and Stochastics 2:215–258.
   Google Scholar
• Karatzas, I., and Shreve, S. E. 1998. Methods of Mathematical Finance. New York: Springer.
   Google Scholar
• King, A. J. 2002. Duality and martingales: A stochastic programming perspective on contingent claims. Mathematical Programming Series B 91:543–562.
   Web of Science ®Google Scholar
• King, A. J., and Korf, L. 2001. Martingale pricing measures in incomplete markets via stochastic programming duality in the dual of . University of Washington. [Preprint]
   Google Scholar
• Klein, I., and Rogers, L. C. G. 2007. Duality in optimal investment and consumption problems with market frictions. Mathematical Finance 17:225–247.
   Web of Science ®Google Scholar
• Kramkov, D., and Schachermayer, W. 1999. The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Annals of Applied Probability 9:904–950.
   Web of Science ®Google Scholar
• Kramkov, D., and Schachermayer, W. 2003. Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 13:1504–1516.
   Web of Science ®Google Scholar
• Øksendal, B. 2007. Stochastic Differential Equations. Berlin: Springer.
   Google Scholar
• Pennanen, T. 2011. Convex duality in stochastic optimization and mathematical finance. Mathematics of Operations Research 36:340–362.
   Web of Science ®Google Scholar
• Pennanen, T. 2012. Dual representation of superhedging costs in illiquid markets. Mathematics and Financial Economics 5:233-248.
   Google Scholar
• Pennanen, T. 2012. Introduction to convex optimization in financial markets. Mathematical Programming 134:157-186.
   Web of Science ®Google Scholar
• Pennanen, T., and Perkkiö, A. P. 2012. Stochastic programs without duality gaps. Mathematical Programming 136:91–110.
   Web of Science ®Google Scholar
• Pham, H. 2009. Continuous-Time Stochastic Control and Optimization with Financial Applications. Berlin: Springer.
   Google Scholar
• Pinar, M. Ç. 2012. A dual representation of gain-loss hedging for european claims in discrete time. Optimization 61:361–372.
   Web of Science ®Google Scholar
• Pinar, M. Ç. 2010. Gain-loss pricing under ambiguity of measure. SAIM: Control, Optimization and Calculus of Variations. 16:132–147.
   Web of Science ®Google Scholar
• Pliska. S. R. 1997. Introduction to Mathematical Finance: Discrete Time Models. Malden, UK: Blackwell.
   Google Scholar
• Pulido, S. 2011. The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short selling prohibitions. arXiv:1012.3102.
   Google Scholar
• Rockafellar, R. T. 1974. Conjugate Duality and Optimization. Philadelphia: SIAM.
   Google Scholar
• Rockafellar, R. T. 1972. Convex Analysis. Princeton, NJ: Princeton University Press.
   Google Scholar
• Rockafellar, R. T., and Wets, R. J.-B. 2004. Variational Analysis. Berlin: Springer.
   Google Scholar
• Rogers, L. C. G. 2003. Duality in Constrained Optimal Investment and Consumption Problems: A Synthesis. Lecture Notes in Mathematics. Berlin: Springer.
   Google Scholar
• Rogers, L. C. G. 2010. Dual valuation and hedging of bermudan options. SIAM Journal of Financial Mathematics 1:604–608.
   Web of Science ®Google Scholar
• Shapiro, A., Dentcheva, D., and Ruszczyński, A. 2009. Lectures on Stochastic Programming: Modeling and Theory. Philadelphia: SIAM and MPS.
   Google Scholar
• Shilling, R. L. 2005. Measures, Integrals and Martingales. Cambridge, U.K: Cambridge University Press.
   Google Scholar
• Vanderbei, R. J. 1996. Linear Programming: Foundations and Extensions. Boston: Kluwer.
   Google Scholar