✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.