Two explicit Skorokhod embeddings for simple symmetric random walk
Motivated by problems in behavioural finance, we provide two explicit constructions of a randomized stopping time which embeds a given centred distribution µ on integers into a simple symmetric random walk in a uniformly integrable manner. Our first construction has a simple Markovian structure: at...
| Main Authors: | , , , |
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| Format: | Journal article |
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Elsevier
2018
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| _version_ | 1797092848368091136 |
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| author | He, X Hu, S Obloj, J Zhou, X |
| author_facet | He, X Hu, S Obloj, J Zhou, X |
| author_sort | He, X |
| collection | OXFORD |
| description | Motivated by problems in behavioural finance, we provide two explicit constructions of a randomized stopping time which embeds a given centred distribution µ on integers into a simple symmetric random walk in a uniformly integrable manner. Our first construction has a simple Markovian structure: at each step, we stop if an independent coin with a state-dependent bias returns tails. Our second construction is a discrete analogue of the celebrated Azéma–Yor solution and requires independent coin tosses only when excursions away from maximum breach predefined levels. Further, this construction maximizes the distribution of the stopped running maximum among all uniformly integrable embeddings of µ. |
| first_indexed | 2024-03-07T03:51:54Z |
| format | Journal article |
| id | oxford-uuid:c1918891-ee9f-4c4d-9dad-d44e277c3df2 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:51:54Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:c1918891-ee9f-4c4d-9dad-d44e277c3df22022-03-27T06:02:22ZTwo explicit Skorokhod embeddings for simple symmetric random walkJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c1918891-ee9f-4c4d-9dad-d44e277c3df2Symplectic Elements at OxfordElsevier2018He, XHu, SObloj, JZhou, XMotivated by problems in behavioural finance, we provide two explicit constructions of a randomized stopping time which embeds a given centred distribution µ on integers into a simple symmetric random walk in a uniformly integrable manner. Our first construction has a simple Markovian structure: at each step, we stop if an independent coin with a state-dependent bias returns tails. Our second construction is a discrete analogue of the celebrated Azéma–Yor solution and requires independent coin tosses only when excursions away from maximum breach predefined levels. Further, this construction maximizes the distribution of the stopped running maximum among all uniformly integrable embeddings of µ. |
| spellingShingle | He, X Hu, S Obloj, J Zhou, X Two explicit Skorokhod embeddings for simple symmetric random walk |
| title | Two explicit Skorokhod embeddings for simple symmetric random walk |
| title_full | Two explicit Skorokhod embeddings for simple symmetric random walk |
| title_fullStr | Two explicit Skorokhod embeddings for simple symmetric random walk |
| title_full_unstemmed | Two explicit Skorokhod embeddings for simple symmetric random walk |
| title_short | Two explicit Skorokhod embeddings for simple symmetric random walk |
| title_sort | two explicit skorokhod embeddings for simple symmetric random walk |
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