On portfolio optimisation under drawdown and floor type constraints
<p>This work is devoted to portfolio optimisation problem arising in the context of constrained optimisation. Despite the classical convex constraints imposed on proportion of wealth invested in the stock this work deals with the pathwise constraints. The drawdown constraint requires an invest...
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| Format: | Thesis |
| Idioma: | English |
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2012
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| _version_ | 1826315787416109056 |
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| author | Chernyy, V |
| author2 | Obloj, J |
| author_facet | Obloj, J Chernyy, V |
| author_sort | Chernyy, V |
| collection | OXFORD |
| description | <p>This work is devoted to portfolio optimisation problem arising in the context of constrained optimisation. Despite the classical convex constraints imposed on proportion of wealth invested in the stock this work deals with the pathwise constraints. The drawdown constraint requires an investor's wealth process to dominate a given function of its up-to-date maximum. Typically, fund managers are required to post information about their maximum portfolio drawdowns as a part of the risk management procedure. One of the results of this work connects the drawdown constrained and the unconstrained asymptotic portfolio optimisation problems in an explicit manner. The main tools for achieving the connection are Azema-Yor processes which by their nature satisfy the drawdown condition.</p> <p>The other result deals with the constraint given as a floor process which the wealth process is required to dominate. The motivation arises from the financial market where the class of products serve as a protection from a downfall, e.g. out of the money put options. The main result provides the wealth process which dominates any fraction of a given floor and preserves the optimality.</p> <p>In the second part of this work we consider a problem of a lifetime utility of consumption maximisation subject to a drawdown constraint. One contribution to the existing literature consists of extending the results to incorporate a general drawdown constraint for a case of a zero interest rate market. The second result provides the first heuristic results for a problem in a presence of interest rates which differs qualitatively from a zero interest rate case. Also the last chapter concludes with the conjecture for the general case of the problem.</p> |
| first_indexed | 2024-03-06T19:20:20Z |
| format | Thesis |
| id | oxford-uuid:19dee50e-466b-46b5-83ae-5816d3b27c62 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:32:32Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:19dee50e-466b-46b5-83ae-5816d3b27c622024-12-01T15:44:20ZOn portfolio optimisation under drawdown and floor type constraintsThesishttp://purl.org/coar/resource_type/c_db06uuid:19dee50e-466b-46b5-83ae-5816d3b27c62Mathematical financeProbability theory and stochastic processesEnglishOxford University Research Archive - Valet2012Chernyy, VObloj, J<p>This work is devoted to portfolio optimisation problem arising in the context of constrained optimisation. Despite the classical convex constraints imposed on proportion of wealth invested in the stock this work deals with the pathwise constraints. The drawdown constraint requires an investor's wealth process to dominate a given function of its up-to-date maximum. Typically, fund managers are required to post information about their maximum portfolio drawdowns as a part of the risk management procedure. One of the results of this work connects the drawdown constrained and the unconstrained asymptotic portfolio optimisation problems in an explicit manner. The main tools for achieving the connection are Azema-Yor processes which by their nature satisfy the drawdown condition.</p> <p>The other result deals with the constraint given as a floor process which the wealth process is required to dominate. The motivation arises from the financial market where the class of products serve as a protection from a downfall, e.g. out of the money put options. The main result provides the wealth process which dominates any fraction of a given floor and preserves the optimality.</p> <p>In the second part of this work we consider a problem of a lifetime utility of consumption maximisation subject to a drawdown constraint. One contribution to the existing literature consists of extending the results to incorporate a general drawdown constraint for a case of a zero interest rate market. The second result provides the first heuristic results for a problem in a presence of interest rates which differs qualitatively from a zero interest rate case. Also the last chapter concludes with the conjecture for the general case of the problem.</p> |
| spellingShingle | Mathematical finance Probability theory and stochastic processes Chernyy, V On portfolio optimisation under drawdown and floor type constraints |
| title | On portfolio optimisation under drawdown and floor type constraints |
| title_full | On portfolio optimisation under drawdown and floor type constraints |
| title_fullStr | On portfolio optimisation under drawdown and floor type constraints |
| title_full_unstemmed | On portfolio optimisation under drawdown and floor type constraints |
| title_short | On portfolio optimisation under drawdown and floor type constraints |
| title_sort | on portfolio optimisation under drawdown and floor type constraints |
| topic | Mathematical finance Probability theory and stochastic processes |
| work_keys_str_mv | AT chernyyv onportfoliooptimisationunderdrawdownandfloortypeconstraints |