Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions
Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear (topological) space X in w...
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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MDPI
2020
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| Online Access: | http://hdl.handle.net/10835/7471 |
| _version_ | 1789406284439617536 |
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| author | Cruz Rambaud, Salvador |
| author_facet | Cruz Rambaud, Salvador |
| author_sort | Cruz Rambaud, Salvador |
| collection | DSpace |
| description | Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear (topological) space X in which a (convex) cone C defines a vector ordering. There exist markets for only some of the contingent claims of X which assign a price pi to the marketed claim mi . The main purpose of this paper is to provide some novel algebraic characterizations of the no arbitrage condition and specifically to derive the decomposability of discount functions with this approach. Methods: Traditionally, this topic has been focused from a topological or probabilistic point of view. However, in this manuscript the treatment of this topic has been by using purely algebraic tools. Results: We have characterized the absence of arbitrage by only using algebraic concepts, properties and structures. Thus, we have divided these characterizations into those concerning the preference relation and those involving the cone. Conclusion: This paper has provided some novel algebraic properties of the absence of arbitrage by assuming the most general setting. The additivity of discount functions has been derived as a particular case of the general theory. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-7471 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2020 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-74712023-04-12T19:04:36Z Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions Cruz Rambaud, Salvador arbitrage contingent claim free lunch discount function linear price linear space preference relation cone Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear (topological) space X in which a (convex) cone C defines a vector ordering. There exist markets for only some of the contingent claims of X which assign a price pi to the marketed claim mi . The main purpose of this paper is to provide some novel algebraic characterizations of the no arbitrage condition and specifically to derive the decomposability of discount functions with this approach. Methods: Traditionally, this topic has been focused from a topological or probabilistic point of view. However, in this manuscript the treatment of this topic has been by using purely algebraic tools. Results: We have characterized the absence of arbitrage by only using algebraic concepts, properties and structures. Thus, we have divided these characterizations into those concerning the preference relation and those involving the cone. Conclusion: This paper has provided some novel algebraic properties of the absence of arbitrage by assuming the most general setting. The additivity of discount functions has been derived as a particular case of the general theory. 2020-01-17T07:03:07Z 2020-01-17T07:03:07Z 2019-09-19 info:eu-repo/semantics/article 2227-7390 http://hdl.handle.net/10835/7471 en https://www.mdpi.com/2227-7390/7/9/868 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess MDPI |
| spellingShingle | arbitrage contingent claim free lunch discount function linear price linear space preference relation cone Cruz Rambaud, Salvador Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions |
| title | Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions |
| title_full | Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions |
| title_fullStr | Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions |
| title_full_unstemmed | Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions |
| title_short | Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions |
| title_sort | algebraic properties of arbitrage: an application to additivity of discount functions |
| topic | arbitrage contingent claim free lunch discount function linear price linear space preference relation cone |
| url | http://hdl.handle.net/10835/7471 |
| work_keys_str_mv | AT cruzrambaudsalvador algebraicpropertiesofarbitrageanapplicationtoadditivityofdiscountfunctions |