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Stochastic evolution equations for large portfolios of stochastic volatility models

Abstract:

We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their volatilities are correlated through systemic Brownian motions. We are interested in the loss process that arises in this setting and we prove the existence of a large portfolio limit for the empirical measure process of this system. This limit evolves as a me...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1137/17M111715X

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Department:
St Annes College
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Department:
Oxford, MPLS, Mathematical Institute
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM Journal on Financial Mathematics Journal website
Volume:
8
Issue:
1
Pages:
962–1014
Publication date:
2017-12-19
Acceptance date:
2017-09-18
DOI:
ISSN:
1945-497X
Pubs id:
pubs:731242
URN:
uri:cbbfb95e-7063-44a3-8733-cbf2fc16d07e
UUID:
uuid:cbbfb95e-7063-44a3-8733-cbf2fc16d07e
Local pid:
pubs:731242

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