Convex Duality in Stochastic Optimization and Mathematical Finance
Published Online:15 Apr 2011https://doi.org/10.1287/moor.1110.0485
References
- Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (2005) 6(Society for Industrial and Applied Mathematics (SIAM), Philadelphia) MPS/SIAM Series on OptimizationGoogle Scholar
- The shadow price of information in continuous time decision problems. Stochastics (1987) 22(2):151–186Crossref, Google Scholar
- Infinite-dimensional extension of a theorem of Komlós. Probab. Theory Related Fields (1989) 81(2):185–188Crossref, Google Scholar
- On minimizing a convex function subject to linear inequalities. J. Roy. Statist. Soc. Ser. B. (1955) 17(2):173–184Google Scholar
- Necessary and sufficient conditions for existence of an optimal portfolio. J. Econom. Theory (1974) 8(2):235–247Crossref, Google Scholar
- , Cont R. Expected utility maximization: The dual approach. Encyclopedia of Quantitative Finance (2010) (Wiley, New York) . ForthcomingCrossref, Google Scholar
- A unified framework for utility maximization problems: An Orlicz spaces approach. Ann. Appl. Probab. (2008) 18(3):929–966Crossref, Google Scholar
- Convex Analysis and Measurable Multifunctions (1977) 580(Springer-Verlag, Berlin) Crossref, Google Scholar
- A functional version of the Birkhoff ergodic theorem for a normal integrand: A variational approach. Ann. Probab. (2003) 31(1):63–92Crossref, Google Scholar
- Convex duality in constrained portfolio optimization. Ann. Appl. Probab. (1992) 2(4):767–818Crossref, Google Scholar
- Equivalent martingale measures and no-arbitrage in stochastic securities market models. Stochastics Stochastics Rep. (1990) 29(2):185–201Crossref, Google Scholar
- Linear programming under uncertainty. Management Sci. (1955) 1(3–4):197–206Link, Google Scholar
- Dynamic optimization: A grand unification. Proc. 31st IEEE Conf. Decision and Control (1994) 2Tucson, AZ:2035–2036Google Scholar
- A deterministic approach to stochastic optimal control with application to anticipative control. Stochastics Stochastics Rep. (1992) 40(3&4):203–256Crossref, Google Scholar
- , Kelly F. A deterministic approach to optimal stopping. Probability, Statistics and Optimisation: A Tribute to Peter Whittle (1994) (Wiley, Chichester, UK) 455–466Google Scholar
- The Mathematics of Arbitrage (2006) (Springer Finance, Springer-Verlag, Berlin/Heidelberg) Google Scholar
- Asset pricing and hedging in financial markets with transaction costs: An approach based on the von Neumann-Gale model. Ann. Finance (2006) 2(4):327–355Crossref, Google Scholar
- Convex Analysis and Variational Problems (1976) (North-Holland Publishing Co., Amsterdam) . [Translated from the French, Studies in Mathematics and Its Applications, Vol. 1.]Google Scholar
- Stochastic Finance. de Gruyter Studies in Mathematics (2004) 27(Walter de Gruyter & Co., Berlin) . [Extended ed. Stochastic Finance, An Introduction in Discrete Time.]Crossref, Google Scholar
- Topological Vector Spaces (1973) (Gordon and Breach Science Publishers, New York) . [Translated from the French by Orlando Chaljub, Notes on Mathematics and Its Applications.]Google Scholar
- Pricing American options: A duality approach. Oper. Res. (2004) 52(2):258–270Link, Google Scholar
- Integrals, conditional expectations, and martingales of multivalued functions. J. Multivariate Anal. (1977) 7(1):149–182Crossref, Google Scholar
- Arbitrage and state price deflators in a general intertemporal framework. J. Math. Econom. (2005) 41(6):722–734Crossref, Google Scholar
- Hedging and liquidation under transaction costs in currency markets. Finance Stochastics (1999) 3(2):237–248Crossref, Google Scholar
- Mathematical theory. Markets with Transaction Costs (2009) (Springer Finance, Springer-Verlag, Berlin) Google Scholar
- A teachers' note on no-arbitrage criteria. Séminaire de Probabilités, XXXV (2001) 1755(Springer, Berlin) 149–152Crossref, Google Scholar
- Optimal consumption from investment and random endowment in incomplete semimartingale markets. Ann. Probab. (2003) 31(4):1821–1858Crossref, Google Scholar
- Duality and martingales: A stochastic programming perspective on contingent claims. Math. Programming Ser. B (2002) 91(3):543–562Crossref, Google Scholar
- Duality in optimal investment and consumption problems with market frictions. Math. Finance (2007) 17(2):225–247Crossref, Google Scholar
- A generalization of a problem of Steinhaus. Acta Math. Acad. Sci. Hungary (1967) 18:217–229Crossref, Google Scholar
- Stochastic programming duality: ℒ∞ multipliers for unbounded constraints with an application to mathematical finance. Math. Programming Ser. A (2004) 99(2):241–259Crossref, Google Scholar
- The condition on the asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. (1999) 9(3):904–950Crossref, Google Scholar
- Hedging of portfolio-valued claims under convex transaction costs and portfolio constraints. (2009) . Master's thesis, Humboldt-Universität zu Berlin, BerlinGoogle Scholar
- Arbitrage and deflators in illiquid markets. Finance Stochastics (2011) 15(1):57–83Crossref, Google Scholar
- Superhedging in illiquid markets. Math. Finance (2011) . ForthcomingCrossref, Google Scholar
- Hedging of claims with physical delivery under convex transaction costs. SIAM J. Financial Math. (2010) 1:158–178Crossref, Google Scholar
- Introduction to Mathematical Finance: Discrete Time Models (1997) (Blackwell, Malden, MA) Google Scholar
- Integrals which are convex functionals. Pacific J. Math. (1968) 24(3):525–539Crossref, Google Scholar
- Convex Analysis (1970) 28(Princeton University Press, Princeton, NJ) Princeton Mathematical SeriesCrossref, Google Scholar
- Integrals which are convex functionals. II. Pacific J. Math. (1971) 39(2):439–469Crossref, Google Scholar
- Conjugate Duality and Optimization (1974) (Society for Industrial and Applied Mathematics, Philadelphia) Crossref, Google Scholar
- Integral functionals, normal integrands and measurable selections. Nonlinear Operators and the Calculus of Variations (Summer School, Univ. Libre Bruxelles, Brussels, 1975) (1976) 543(Springer, Berlin) 157–207Crossref, Google Scholar
- Nonanticipativity and L1-martingales in stochastic optimization problems. Math. Programming Stud. (1976) 6:170–187Crossref, Google Scholar
- Measures as Lagrange multipliers in multistage stochastic programming. J. Math. Anal. Appl. (1977) 60(2):301–313Crossref, Google Scholar
- The optimal recourse problem in discrete time: L1-multipliers for inequality constraints. SIAM J. Control Optim. (1978) 16(1):16–36Crossref, Google Scholar
- Deterministic and stochastic optimization problems of Bolza type in discrete time. Stochastics (1983) 10(3–4):273–312Crossref, Google Scholar
- Variational Analysis (1998) 317(Springer-Verlag, Berlin) Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]Crossref, Google Scholar
- Monte Carlo valuation of American options. Math. Finance (2002) 12(3):271–286Crossref, Google Scholar
- The Kreps-Yan theorem for L∞. Int. J. Math. Math. Sci. (2005) 2005(17):2749–2756Crossref, Google Scholar
- A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time. Insurance Math. Econom. (1992) 11(4):249–257Crossref, Google Scholar
- The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time. Math. Finance (2004) 14(1):19–48Crossref, Google Scholar
- Lectures on Stochastic Programming: Modeling and Theory (2009) 9(SIAM, Philadelphia) MPS/SIAM Series on OptimizationCrossref, Google Scholar
- Probability. Graduate Texts in Mathematics (1996) 952nd ed.(Springer-Verlag, New York) . [Translated from the first (1980) Russian edition by R. P. Boas.]Google Scholar
- Pricing contingent claims: A computational compatible approach. (2006) . Working paper, University of California at Davis, DavisGoogle Scholar
- , Bensoussan A., Lions J. L. On the relation between stochastic and deterministic optimization. Control Theory, Numerical Methods and Computer Systems Modelling (1975) 107(Springer, New York) 350–361Crossref, Google Scholar

