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Mathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying. In earlier work [Proc. R. Soc. London, 2004], the first author provided a geometric condition under which trading in the underlying and a finite number of vanilla options completes the market. We complement this result in several ways. First, we show that the geometric condition is not necessary...
We solve explicitly the following problem: for a given probability measure , we specify a generalised martingale diffusion () which, stopped at an independent exponential time , is distributed according to . The process (
) is specified its speed measure . We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, 20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give a proof exploiting...
We solve explicitly the following problem: for a given probability
measure , we specify a generalised martingale diffusion () which, stopped at an independent exponential time , is
distributed according to . The process (
) is specified
its speed measure . We present two heuristic arguments and three
proofs. First we show how
the result can be derived from the solution of [Bertoin and Le Jan,
(1992) 538–548.] to the Skorokhod embedding problem. Secondly,
we...
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