Optimal replication of random claims by ordinary integrals with applications in finance
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 or...
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| Format: | Conference Paper |
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Society for Industrial and Applied Mathematics
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/32673 |
| _version_ | 1848753728447840256 |
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| author | Dokuchaev, Nikolai |
| author2 | n/a |
| author_facet | n/a Dokuchaev, Nikolai |
| author_sort | Dokuchaev, Nikolai |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T08:29:08Z |
| format | Conference Paper |
| id | curtin-20.500.11937-32673 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:29:08Z |
| publishDate | 2013 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-326732017-09-13T15:26:00Z Optimal replication of random claims by ordinary integrals with applications in finance Dokuchaev, Nikolai n/a portfolio selection optimal stochastic control contingent claim replication 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. 2013 Conference Paper http://hdl.handle.net/20.500.11937/32673 10.1137/1.9781611973273.9 Society for Industrial and Applied Mathematics fulltext |
| spellingShingle | portfolio selection optimal stochastic control contingent claim replication Dokuchaev, Nikolai Optimal replication of random claims by ordinary integrals with applications in finance |
| title | Optimal replication of random claims by ordinary integrals with applications in finance |
| title_full | Optimal replication of random claims by ordinary integrals with applications in finance |
| title_fullStr | Optimal replication of random claims by ordinary integrals with applications in finance |
| title_full_unstemmed | Optimal replication of random claims by ordinary integrals with applications in finance |
| title_short | Optimal replication of random claims by ordinary integrals with applications in finance |
| title_sort | optimal replication of random claims by ordinary integrals with applications in finance |
| topic | portfolio selection optimal stochastic control contingent claim replication |
| url | http://hdl.handle.net/20.500.11937/32673 |