Kardaras, Constantinos ORCID: 0000-0001-6903-4506
(2023)
*Stochastic integration with respect to arbitrary collections of continuous semimartingales and applications to mathematical finance.*
Annals of Applied Probability.
ISSN 1050-5164
(In Press)

Text (Stochastic integration with respect to arbitrary collections of continuous semimartingales and applications to mathematical finance)
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## Abstract

Stochastic integrals are defined with respect to a collection P = (Pi; i 2 I) of continuous semimartingales, imposing no assumptions on the index set I and the subspace of RI where P takes values. The integrals are constructed though finite-dimensional approximation, identifying the appropriate local geometry that allows extension to infinite dimensions. For local martingale integrators, the resulting space S(P) of stochastic integrals has an operational characterisation via a corresponding set of integrands R(C), constructed with only reference the covariation structure C of P. This bijection between R(C) and the (closed in the semimartingale topology) set S(P) extends to families of continuous semimartingale integrators for which the drift process of P belongs to R(C). In the context of infinite-asset models in Mathematical Finance, the latter structural condition is equivalent to a certain natural form of market viability. The enriched class of wealth processes via extended stochastic integrals leads to exact analogues of optional decomposition and hedging duality as the finite-asset case. A corresponding characterisation of market completeness in this setting is provided.

Item Type: | Article |
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Official URL: | https://projecteuclid.org/journals/annals-of-appli... |

Additional Information: | © 2023 Institute of Mathematical Statistics |

Divisions: | Statistics |

Subjects: | H Social Sciences > HA Statistics |

Date Deposited: | 14 Dec 2023 16:09 |

Last Modified: | 20 May 2024 10:27 |

URI: | http://eprints.lse.ac.uk/id/eprint/121057 |

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