Some Divergence Properties of Asset Price Models
Abstract: We consider asset price processes Xt which are weak solutions of one-dimensional stochastic differential equations of the form (equation (2)) Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownian motion. We study properties of the IÃŽ...
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| Format: | Article |
| Language: | English |
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MDPI AG
2001-12-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/3/5/300/ |
| _version_ | 1817996617342517248 |
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| author | Wolfgang Stummer |
| author_facet | Wolfgang Stummer |
| author_sort | Wolfgang Stummer |
| collection | DOAJ |
| description | Abstract: We consider asset price processes Xt which are weak solutions of one-dimensional stochastic differential equations of the form (equation (2)) Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownian motion. We study properties of the Iα-divergence between the law of the solution Xt and the corresponding drift-less measure (the special case α=1 is the relative entropy). This will be applied to some context in statistical information theory as well as to arbitrage theory and contingent claim valuation. For instance, the seminal option pricing theorems of Black-Scholes and Merton appear as a special case. |
| first_indexed | 2024-04-14T02:24:59Z |
| format | Article |
| id | doaj.art-0395207d8c9244f985291246a01fd2d9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T02:24:59Z |
| publishDate | 2001-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0395207d8c9244f985291246a01fd2d92022-12-22T02:17:54ZengMDPI AGEntropy1099-43002001-12-013530032410.3390/e3050300Some Divergence Properties of Asset Price ModelsWolfgang StummerAbstract: We consider asset price processes Xt which are weak solutions of one-dimensional stochastic differential equations of the form (equation (2)) Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownian motion. We study properties of the Iα-divergence between the law of the solution Xt and the corresponding drift-less measure (the special case α=1 is the relative entropy). This will be applied to some context in statistical information theory as well as to arbitrage theory and contingent claim valuation. For instance, the seminal option pricing theorems of Black-Scholes and Merton appear as a special case.http://www.mdpi.com/1099-4300/3/5/300/Iα-divergencerelative entropystatistical informationequivalent martingale measureoption pricingBlack-Scholes-Merton |
| spellingShingle | Wolfgang Stummer Some Divergence Properties of Asset Price Models Entropy Iα-divergence relative entropy statistical information equivalent martingale measure option pricing Black-Scholes-Merton |
| title | Some Divergence Properties of Asset Price Models |
| title_full | Some Divergence Properties of Asset Price Models |
| title_fullStr | Some Divergence Properties of Asset Price Models |
| title_full_unstemmed | Some Divergence Properties of Asset Price Models |
| title_short | Some Divergence Properties of Asset Price Models |
| title_sort | some divergence properties of asset price models |
| topic | Iα-divergence relative entropy statistical information equivalent martingale measure option pricing Black-Scholes-Merton |
| url | http://www.mdpi.com/1099-4300/3/5/300/ |
| work_keys_str_mv | AT wolfgangstummer somedivergencepropertiesofassetpricemodels |