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On SDEs with marginal laws evolving in finite-dimensional exponential families

✍ Scribed by Damiano Brigo


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
105 KB
Volume
49
Category
Article
ISSN
0167-7152

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✦ Synopsis


In the present paper, given a di usion coe cient and a curve in an exponential family, we deÿne a drift such that the density of the resulting di usion process evolves in the prescribed exponential family according to the given curve. As an application to mathematical ÿnance, we construct a family of stock price processes that are equivalent in discrete time while implying arbitrary prices for options written on them. As an application to nonlinear ÿltering, we construct nonlinear ÿltering problems admitting a ÿnite-dimensional ÿlter.