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

Damiano Brigo

Statistics & Probability Letters, 2000, vol. 49, issue 2, 127-134

Abstract: In the present paper, given a diffusion coefficient and a curve in an exponential family, we define a drift such that the density of the resulting diffusion process evolves in the prescribed exponential family according to the given curve. As an application to mathematical finance, 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 filtering, we construct nonlinear filtering problems admitting a finite-dimensional filter.

Keywords: Stochastic; differential; equations; Exponential; families; Stock; price; models; Option; pricing; Nonlinear; filtering; Finite; dimensional; filters (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (5)

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