Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation.
We study optimal investment problem for a market model where the evolution of risky assets prices is described by Itoˆs equations. The risk-free rate, the appreciation rates, and the volatility of the stocks are all random; they depend on a random parameter that is not adapted to the driving Brownia...
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| Format: | Journal Article |
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Oxford University Press
2006
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| Online Access: | http://hdl.handle.net/20.500.11937/41201 |
| _version_ | 1848756079078408192 |
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| author | Dokuchaev, Nikolai |
| author_facet | Dokuchaev, Nikolai |
| author_sort | Dokuchaev, Nikolai |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We study optimal investment problem for a market model where the evolution of risky assets prices is described by Itoˆs equations. The risk-free rate, the appreciation rates, and the volatility of the stocks are all random; they depend on a random parameter that is not adapted to the driving Brownian motion. The distribution of this parameter is unknown. The optimal investment problem is stated in a mazimin setting to ensure that a strategy is found such that the minimum of expected utility over all possible distributions of parameters is maximal. We show that a saddle point exists and can be found via solution of the standard one-dimensional heat equation with a Cauchy condition defined via one-dimensional minimization. This solution even covers models with unknown solution for a given distribution of the market parameters. |
| first_indexed | 2025-11-14T09:06:29Z |
| format | Journal Article |
| id | curtin-20.500.11937-41201 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:06:29Z |
| publishDate | 2006 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-412012019-02-19T05:35:12Z Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. Dokuchaev, Nikolai continuous time market models saddle point - minimax problems optimal portfolio uncertainty We study optimal investment problem for a market model where the evolution of risky assets prices is described by Itoˆs equations. The risk-free rate, the appreciation rates, and the volatility of the stocks are all random; they depend on a random parameter that is not adapted to the driving Brownian motion. The distribution of this parameter is unknown. The optimal investment problem is stated in a mazimin setting to ensure that a strategy is found such that the minimum of expected utility over all possible distributions of parameters is maximal. We show that a saddle point exists and can be found via solution of the standard one-dimensional heat equation with a Cauchy condition defined via one-dimensional minimization. This solution even covers models with unknown solution for a given distribution of the market parameters. 2006 Journal Article http://hdl.handle.net/20.500.11937/41201 10.1093/imaman/dpi041 Oxford University Press fulltext |
| spellingShingle | continuous time market models saddle point - minimax problems optimal portfolio uncertainty Dokuchaev, Nikolai Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. |
| title | Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. |
| title_full | Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. |
| title_fullStr | Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. |
| title_full_unstemmed | Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. |
| title_short | Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. |
| title_sort | saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. |
| topic | continuous time market models saddle point - minimax problems optimal portfolio uncertainty |
| url | http://hdl.handle.net/20.500.11937/41201 |