This pages lists references and links related to (convex) optimization theory and its applications in financial engineering.
Books
Gerard Cornuejols and Reha Tütüncü, Optimization Methods in Finance. Cambridge University Press (2007).
Boyd, S. and L. Vandenberghe, Convex Optimization, (2004) Cambridge University Press. The full book is available online here.
Ben-Tal, A. and A. Nemirovski, Lectures on modern convex optimization : analysis, algorithms, and engineering applications. MPS-SIAM series on optimization. 2001, Philadelphia, PA: Society for Industrial and Applied Mathematics : Mathematical Programming Society. xvi, 488.
Borwein, J.M. and A.S. Lewis, Convex analysis and nonlinear optimization : theory and examples. CMS books in mathematics ; 3. 2000, New York: Springer. x, 273.
Nesterov, Y. and A. Nemirovskii, Interior-point polynomial algorithms in convex programming. 1994, Philadelphia: Society for Industrial and Applied Mathematics. ix, 405.
Surveys & Lecture Notes
Cont, R., Inverse Problems in financial modeling: theoretical and numerical aspects of model calibration. Lecture Notes, Princeton University., 2001.
Vandenberghe, L. and S. Boyd, Semidefinite programming. SIAM Review, 1996. 38: p. 49--95.
Papers
Avellaneda, M., et al., Reconstruction of volatility: Pricing index options using the steepest-descent approximation. Risk Magazine, 2002.
Avellaneda, M., et al., Calibrating Volatility Surfaces via Relative Entropy Minimization. Applied Mathematical Finance, 1997. 4(1): p. 37-64.
Avellaneda, M., A. Levy, and A. Paras, Pricing and hedging derivative securities in markets with uncertain volatilities. Applied Mathematical Finance, 1995. 2: p. 73-88.
Avellaneda, M. and A. Paras, Managing the volatility risk of portfolios of derivative securities: the Lagrangian Uncertain Volatility Model. Applied Mathematical Finance, 1996. 3: p. 21-52.
Bally, V. and G. Pages, A quantization algorithm for solving multi-dimensional Optimal Stopping problems. Preprint 628, Laboratoire de Probabilites, University de Paris VI., 2000.
Ben-Tal, A., L. El Ghaoui, and H. Lebret, Robust Semidefinite Programming, in Handbook on Semidefinite Programming, S. Sastry, H. Wolkowitcz, and L. Vandenberghe, Editors. 1998.
Berg, C., The multidimensional moment problem and semi-groups, in Moments in Mathematics, H.J. Landau, Editor. 1980, AMS: Providence, RI. p. 110-124.
Bertsimas, D. and I. Popescu, On the Relation between Option and Stock Prices: a Convex Optimization Approach. Operations Research, 2002. 50(2): p. 358-374.
Boyd, S.P., M. Fazel, and H. Hindi, A rank minimization heuristic with application to minimum order system approximation. American Control Conference, 2000.
Brace, A., T. Dun, and G. Barton, Towards a Central Interest Rate Model. Working Paper. FMMA, 1999.
Brace, A. and R.S. Womersley, Exact fit to the swaption volatility matrix using semidefinite programming. Working paper, ICBI Global Derivatives Conference, 2000.
Breeden, D.T. and R.H. Litzenberger, Price of State-Contingent Claims Implicit in Option Prices. Journal of Business, 1978. 51(4): p. 621-651.
Brigo, D., et al., Approximated moment-matching dynamics for basket-options pricing. Quantitative Finance, 2004. 4: p. 1-16.
Broadie, M. and P. Glasserman, Pricing American-Style Securities by Simulation. J. Economic Dynamics and Control, 1997. 21: p. 1323-1352.
Buchen, P.W. and M. Kelly, The maximum entropy distribution of an asset inferred from option prices. Journal of Financial and Quantitative Anaysis, 1996. 31: p. 143-159.
d'Aspremont, A., Interest rate model calibration using semidefinite programming. Applied Mathematical Finance, 2003. 10(3): p. 183-213. (Warning: shameless self-promotion)
d'Aspremont, A., A Harmonic Analysis Solution to the Static Basket Arbitrage Problem. ArXiv: math.OC/0309048, 2003. (Warning: shameless self-promotion)
d'Aspremont, A. and L. El Ghaoui, Static arbitrage bounds on basket option prices. EECS Technical report, UC Berkeley. ArXiv: math.OC/0302243, 2002. (Warning: shameless self-promotion)
Edirisinghe, C., V. Naik, and R. Uppal, Optimal Replication of Options with Transactions Costs and Trading Restrictions. Journal of Financial and Quantitative Analysis, 1993. 28(1): p. 117-138.
El Karoui, N., M. Jeanblanc-Picqu\'e, and S.E. Shreve, On the Robustness of the Black-Scholes Equation. Mathematical Finance, 1998. 8: p. 93-126.
El Karoui, N. and M.C. Quenez, Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market. Siam Journal of Control and Optimization, 1995. 33: p. 29-66.
Henkin, G. and A. Shananin, Bernstein theorems and Radon transform, application to the theory of production functions. American Mathematical Society: Translation of mathematical monographs, 1990. 81: p. 189-223.
Hettich, R. and K.O. Kortanek, Semi-Infinite Programming: Theory, Methods and Applications. SIAM Review, 1993. 35(3): p. 380-429.
Hobson, D., P. Laurence, and T.H. Wang, Static Arbitrage Upper Bounds for the Prices of Basket Options. Working paper, 2004.
Hodges, S. and A. Neuberger, Optimal Replication of Contingent Claims under Transaction Costs. Review of Futures Markets, 1989. 8: p. 222-239.
Jackwerth, J. and M. Rubinstein, Recovering Probability Distributions from Option Prices. Journal of Finance, 1996. 51(5): p. 1611-1631.
Lobo, M., et al., Applications of second-order cone programming. Linear Algebra and its Applications, 1998. 284: p. 193-228.
Mirrlees, J.A., An exploration of the theory of optimum income taxation. Review of economic studies, 1971. 38: p. 175-208.
Mittelmann, H.D., An independent benchmarking of {SDP} and {SOCP} solvers. Mathematical Programming Series B, 2003. 95(2): p. 407-430.
Rogers, L.C.G., Monte Carlo valuation of American options. Mathematical Finance, 2002. 12(3): p. 271.
Rouge, R. and N. El Karoui, Pricing via Utility Maximization and Entropy. Mathematical Finance, 2000. 10(2): p. 259-276.
Software
SEDUMI, a software package for linear, quadratic, second-order cone & semidefinite programming (GPL license).
MOSEK, a software package for convex and mixed-integer programming (Commercial, free for academic use).
This page is maintained by Alexandre d'Aspremont. If you think of a reference that should appear in this list, please email it to me (in bibtex format preferably).