51 research outputs found
Existence and uniqueness results for BSDEs with jumps: the whole nine yards
This paper is devoted to obtaining a wellposedness result for
multidimensional BSDEs with possibly unbounded random time horizon and driven
by a general martingale in a filtration only assumed to satisfy the usual
hypotheses, i.e. the filtration may be stochastically discontinuous. We show
that for stochastic Lipschitz generators and unbounded, possibly infinite, time
horizon, these equations admit a unique solution in appropriately weighted
spaces. Our result allows in particular to obtain a wellposedness result for
BSDEs driven by discrete--time approximations of general martingales.Comment: 48 pages, final version, forthcoming in the Electronic Journal of
Probabilit
Esscher transform and the duality principle for multidimensional semimartingales
The duality principle in option pricing aims at simplifying valuation
problems that depend on several variables by associating them to the
corresponding dual option pricing problem. Here, we analyze the duality
principle for options that depend on several assets. The asset price processes
are driven by general semimartingales, and the dual measures are constructed
via an Esscher transformation. As an application, we can relate swap and quanto
options to standard call and put options. Explicit calculations for jump models
are also provided.Comment: Published in at http://dx.doi.org/10.1214/09-AAP600 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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