A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA
We study the question what value an agent in a generalized Black-Scholes model with partial information attributes to the complementary information. To do this, we study the utility maximization problems from terminal wealth for the two cases partial information and full information. We assume that...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2011/238623 |
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| author | Zhaojun Yang Christian-Oliver Ewald Wen-Kai Wang |
| author_facet | Zhaojun Yang Christian-Oliver Ewald Wen-Kai Wang |
| author_sort | Zhaojun Yang |
| collection | DOAJ |
| description | We study the question what value an agent in a generalized Black-Scholes model with partial information attributes to the complementary information. To do this, we study the utility maximization problems from terminal wealth for the two cases partial information and full information. We assume that the drift term of the risky asset is a dynamic process of general linear type and that the two levels of observation correspond to whether this drift term is observable or not. Applying methods from stochastic filtering theory we derive an analytical tractable formula for the value of information in the case of logarithmic utility. For the case of constant relative risk aversion (CRRA) we derive a semianalytical formula, which uses as an input the numerical solution of a system of ODEs. For both cases we present a comparative analysis. |
| format | Article |
| id | doaj-art-86865e18049f48fd9e1ff991893d5468 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-86865e18049f48fd9e1ff991893d54682025-02-03T01:11:48ZengWileyJournal of Probability and Statistics1687-952X1687-95382011-01-01201110.1155/2011/238623238623A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRAZhaojun Yang0Christian-Oliver Ewald1Wen-Kai Wang2School of Finance and Statistics, Hunan University, Changsha 410079, ChinaSchool of Mathematics and Statistics, University of Sydney, Sydney NSW 2006, AustraliaSchool of Mathematics and Statistics, University of Sydney, Sydney NSW 2006, AustraliaWe study the question what value an agent in a generalized Black-Scholes model with partial information attributes to the complementary information. To do this, we study the utility maximization problems from terminal wealth for the two cases partial information and full information. We assume that the drift term of the risky asset is a dynamic process of general linear type and that the two levels of observation correspond to whether this drift term is observable or not. Applying methods from stochastic filtering theory we derive an analytical tractable formula for the value of information in the case of logarithmic utility. For the case of constant relative risk aversion (CRRA) we derive a semianalytical formula, which uses as an input the numerical solution of a system of ODEs. For both cases we present a comparative analysis.http://dx.doi.org/10.1155/2011/238623 |
| spellingShingle | Zhaojun Yang Christian-Oliver Ewald Wen-Kai Wang A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA Journal of Probability and Statistics |
| title | A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA |
| title_full | A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA |
| title_fullStr | A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA |
| title_full_unstemmed | A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA |
| title_short | A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA |
| title_sort | comparative analysis of the value of information in a continuous time market model with partial information the cases of log utility and crra |
| url | http://dx.doi.org/10.1155/2011/238623 |
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