-
called a
semimartingale if it can be
decomposed as the sum of a
local martingale and a càdlàg
adapted finite-variation process.
Semimartingales are "good...
-
integral or Fisk–Stratonovich
integral of a
semimartingale X {\displaystyle X}
against another semimartingale Y can be
defined in
terms of the Itô integral...
- connection: We can then
introduce the
stochastic horizontal lift of a
semimartingale and the
stochastic development by the so-called Eells-Elworthy-Malliavin...
- 1999,
Chapter IV),
which is a
Brownian motion or, more generally, a
semimartingale. The
result of the
integration is then
another stochastic process. Concretely...
-
generally a
semimartingale. However,
other types of
random behaviour are possible, such as jump
processes like Lévy
processes or
semimartingales with jumps...
- calculus, the Doléans-Dade
exponential or
stochastic exponential of a
semimartingale X is the
unique strong solution of the
stochastic differential equation...
-
price process is ****umed to
follow a more
general sigma-martingale or
semimartingale, then the
concept of
arbitrage is too narrow, and a
stronger concept...
- is
absolutely continuous with
respect to P then
every P-
semimartingale is a Q-
semimartingale. We
state the
theorem first for the
special case when the...
- be
applied to
general d-dimensional
semimartingales,
which need not be continuous. In general, a
semimartingale is a càdlàg process, and an additional...
- predictability. The
theory also
extends Itô's
theory of SDEs far
beyond the
semimartingale setting. At the
heart of the
mathematics is the
challenge of describing...
