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

Nikolai Dokuchaev

Papers from arXiv.org

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.

Date: 2013-01, Revised 2013-01
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Published in SIAM Conference on Control and Its Applications, Jul 8, 2013, San Diego, California USA: Society for Industrial and Applied Mathematics;pp. 59-66

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1301.0381

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