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Viscosity Solutions of Integro-Differential Equations and Passport Options in a Jump-Diffusion Model

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Abstract

We study the viscosity solutions of integro-differential Hamilton–Jacobi–Bellman equations of degenerate parabolic type. These equations are from the pricing problem for the European passport options in a jump-diffusion model. The passport option is a call option on a trading account. We discuss the mathematical model for pricing problem. We prove the comparison principle, uniqueness and convexity preserving for the viscosity solutions of related pricing equations.

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Acknowledgements

This work was supported in part by the Research Program of Shanghai Normal University (No. SK201211), the Major Project of Shanghai Municipal Education Commission (No. 13ZZ107) and Shanghai Normal University Leading Academic Discipline Project (No. DZW912). The authors would like to thank the reviewers for their very helpful comments and suggestions.

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Authors and Affiliations

  1. Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, P.R. China

    Yang Wang & Jizhou Zhang

  2. Department of Mathematics, Tongji University, Shanghai, 200092, P.R. China

    Baojun Bian

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  1. Yang Wang
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  2. Baojun Bian
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  3. Jizhou Zhang
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Correspondence to Yang Wang.

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Wang, Y., Bian, B. & Zhang, J. Viscosity Solutions of Integro-Differential Equations and Passport Options in a Jump-Diffusion Model. J Optim Theory Appl 161, 122–144 (2014). https://doi.org/10.1007/s10957-013-0382-9

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  • DOI: https://doi.org/10.1007/s10957-013-0382-9

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