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    Optimal replication of random claims by ordinary integrals with applications in finance

    191963_93905_procSIAM2013my.pdf (228.1Kb)
    Access Status
    Open access
    Authors
    Dokuchaev, Nikolai
    Date
    2013
    Type
    Conference Paper
    
    Metadata
    Show full item record
    Citation
    Dokuchaev, Nikolai. 2013. Optimal replication of random claims by ordinary integrals with applications in finance, in Fahroo, F. and Kang, W. and Zhang, Q., Proceedings of the Conference on Control and Its Applications (CT13), Jul 8-10 2013, pp. 59-66. San Diego, California: Society for Industrial and Applied Mathematics.
    Source Title
    Proceedings of the SIAM Conference on Control and Its Applications (CT13), San Diego, California, USA, July 8-10, 2013.
    Source Conference
    SIAM Conference on Control and Its Applications
    DOI
    10.1137/1.9781611973273.9
    ISSN
    23266627
    Remarks

    Copyright © 2013 SIAM. Published with permission.

    URI
    http://hdl.handle.net/20.500.11937/32673
    Collection
    • Curtin Research Publications
    Abstract

    By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via adapted differentiable processes generated by a controlled ordinary differential equation. We found that the solution of this replication problem exists and is not unique. This leads to a new optimal control problem: find a replicating process that is minimal in an integral norm. We found an explicit solution of this problem. Possible applications to portfolio selection problems and to bond pricing models are suggested.

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