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

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  • Nikolai Dokuchaev

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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  • Nikolai Dokuchaev, 2013. "Optimal replication of random claims by ordinary integrals with applications in finance," Papers 1301.0381, arXiv.org, revised Jan 2013.
    • Handle: RePEc:arx:papers:1301.0381
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    References listed on IDEAS

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    1. Dickson, David C.M. & Waters, Howard R., 2004. "Some Optimal Dividends Problems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 49-74, May.
    2. Nikolai Dokuchaev, 2010. "Optimal gradual liquidation of equity from a risky asset," Applied Economics Letters, Taylor & Francis Journals, vol. 17(13), pages 1305-1308.
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    Cited by:

    1. Renko Siebols, 2017. "Cash Accumulation Strategy based on Optimal Replication of Random Claims with Ordinary Integrals," Papers 1711.01756, arXiv.org.

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