On the uniqueness of classical solutions of Cauchy problems

DOI10.1090/S0002-9939-10-10306-2zbMath1194.35012arXiv0908.1086MaRDI QIDQ3566668

Hao Xing, Erhan Bayraktar

Publication date: 8 June 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.1086

zbMATH Keywords

strict local martingalesa necessary and sufficient condition for uniquenessEuropean call-type options

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Martingales with continuous parameter (60G44) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (10)

Uniqueness in Cauchy problems for diffusive real-valued strict local martingales ⋮ Distribution of the time to explosion for one-dimensional diffusions ⋮ Diffusion transformations, Black-Scholes equation and optimal stopping ⋮ On the Feller-Dynkin and the martingale property of one-dimensional diffusions ⋮ On backward stochastic differential equations and strict local martingales ⋮ Outperforming the market portfolio with a given probability ⋮ The stochastic solution to a Cauchy problem for degenerate parabolic equations ⋮ Strict local martingale deflators and valuing American call-type options ⋮ Approximating functionals of local martingales under lack of uniqueness of the Black–Scholes PDE solution ⋮ A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

Cites Work

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• Bubbles, convexity and the Black-Scholes equation
• No arbitrage condition for positive diffusion price processes
• Strict local martingale deflators and valuing American call-type options
• Local martingales, bubbles and option prices

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