Revisiting Semidefinite Programming Approaches to Options Pricing: Complexity and Computational Perspectives
Published Online:5 Jan 2023https://doi.org/10.1287/ijoc.2022.1220
References
- (2002) On the relation between option and stock prices: A convex optimization approach. Oper. Res. 50(2):358–374.Link, Google Scholar
- (2020) The core variety and representing measures in the truncated moment problem. J. Operator Theory 84(1):185–209.Crossref, Google Scholar
- (1996) Semidefinite programming. SIAM Rev. 38(1):49–95.Crossref, Google Scholar
- (1997) Bounds on contingent claims based on several assets. J. Financial Econom. 46(3):383–400.Crossref, Google Scholar
- (1976) The valuation of options for alternative stochastic processes. J. Financial Econom. 3(1):145–166.Crossref, Google Scholar
- (2004) Shape constrained optimization with application in finance and engineering. Unpublished PhD thesis, Stanford University, Stanford, CA.Google Scholar
- (2007) The range of traded option prices. Math. Finance 17(1):1–14.Crossref, Google Scholar
- (2019) A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis, Association for Women in Mathematics Series (Springer), 17–56.Google Scholar
- (2020) Distributionally robust optimization with polynomial densities: Theory, models and algorithms. Math. Programming 181(2):265–296.Crossref, Google Scholar
- (2018) The multidimensional truncated moment problem: Atoms, determinacy, and core variety. J. Functional Anal. 274(11):3124–3148.Crossref, Google Scholar
- (1979) Martingales and arbitrage in multiperiod securities markets. J. Econom. Theory 20(3):381–408.Crossref, Google Scholar
- (2022) OptionsPricing version v1.0 http://dx.doi.org/10.5281/zenodo.6602361.Google Scholar
- (2005a) Static-arbitrage optimal subreplicating strategies for basket options. Insurance Math. Econom. 37(3):553–572.Crossref, Google Scholar
- (2005b) Static-arbitrage upper bounds for the prices of basket options. Quant. Finance 5(4):329–342.Crossref, Google Scholar
- (1906) Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica 30(1):175–193.Crossref, Google Scholar
- (2008) A semidefinite programming approach to the generalized problem of moments. Math. Programming 112(1):65–92.Crossref, Google Scholar
- (2009) Moments, Positive Polynomials and Their Applications (Imperial College Press, Singapore).Crossref, Google Scholar
- (2010) A new look at nonnegativity on closed sets and polynomial optimization. SIAM J. Optim. 21(3):796–817.Crossref, Google Scholar
- (2005) Sharp upper and lower bounds for basket options. Appl. Math. Finance 12(3):253–282.Crossref, Google Scholar
- (2005) Bounding option prices of multi-assets: A semidefinite programming approach. Pacific J. Optim. 1:59–79.Google Scholar
- (1987) Semi-parametric upper bounds for option prices and expected payoffs. J. Financial Econom. 19(2):373–387.Crossref, Google Scholar
- (1973) The theory of rational option pricing. Bell J. Econom. Management Sci. 4(1):141–183.Crossref, Google Scholar
- MOSEK (2019) MOSEK optimization software. Technical report, version 9.1.9. http://docs.mosek.com/9.1/toolbox/index.html.Google Scholar
- (2014) Optimality conditions and finite convergence of Lasserre’s hierarchy. Math. Programming 146(1):97–121.Crossref, Google Scholar
- (2005) A conic programming approach to generalized Tchebycheff inequalities. Math. Oper. Res. 30(2):369–388.Link, Google Scholar
- (2006) Option pricing bounds via semidefinite programming. Proc. Amer. Control Conf., 6.Google Scholar
- (1956) Convergence of random processes and limit theorems in probability theory. Theory Probab. Appl. 1(2):157–214.Crossref, Google Scholar
- (1957) Parameterfreie Abschätzung und Realisierung von Erwartungswerten. Blätter DGVFM 3:147–162.Crossref, Google Scholar
- (2001) Semi-infinite programming: Recent advances. Goberna M, López MA, eds. On Duality Theory of Conic Linear Problems (Springer US, Boston), 135–165.Crossref, Google Scholar
- (2021) Convergence of Lasserre’s hierarchy: The general case. Optim. Lett. 16:1015–1033.Crossref, Google Scholar
- (2019) MomentOpt.jl. Polynomial and moment optimization in Julia and JuMP, v0.2.0. https://pretalx.com/juliacon2019/talk/QZBKAU/.Google Scholar

