Distributional Replication
A function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under sui...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/8/1063 |
| _version_ | 1797523894432694272 |
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| author | Brendan K. Beare |
| author_facet | Brendan K. Beare |
| author_sort | Brendan K. Beare |
| collection | DOAJ |
| description | A function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under suitable regularity conditions, including a bound on the entropy of the set of candidate approximations, we show that the optimal approximation comes close to achieving distributional replication, and close to achieving the minimum cost among replicating functions. We discuss the relevance of our results to the financial literature on hedge fund replication; in this case, the optimal approximation corresponds to the cheapest portfolio of market index options which delivers the hedge fund return distribution. |
| first_indexed | 2024-03-10T08:49:36Z |
| format | Article |
| id | doaj.art-4705834d186846818313da06c3d0c9f6 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T08:49:36Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-4705834d186846818313da06c3d0c9f62023-11-22T07:35:45ZengMDPI AGEntropy1099-43002021-08-01238106310.3390/e23081063Distributional ReplicationBrendan K. Beare0School of Economics, University of Sydney, Sydney, NSW 2006, AustraliaA function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under suitable regularity conditions, including a bound on the entropy of the set of candidate approximations, we show that the optimal approximation comes close to achieving distributional replication, and close to achieving the minimum cost among replicating functions. We discuss the relevance of our results to the financial literature on hedge fund replication; in this case, the optimal approximation corresponds to the cheapest portfolio of market index options which delivers the hedge fund return distribution.https://www.mdpi.com/1099-4300/23/8/1063distributional replicationsieve estimationhedge fund replication |
| spellingShingle | Brendan K. Beare Distributional Replication Entropy distributional replication sieve estimation hedge fund replication |
| title | Distributional Replication |
| title_full | Distributional Replication |
| title_fullStr | Distributional Replication |
| title_full_unstemmed | Distributional Replication |
| title_short | Distributional Replication |
| title_sort | distributional replication |
| topic | distributional replication sieve estimation hedge fund replication |
| url | https://www.mdpi.com/1099-4300/23/8/1063 |
| work_keys_str_mv | AT brendankbeare distributionalreplication |