2,366 research outputs found
A Donsker delta functional approach to optimal insider control and applications to finance
We study \emph{optimal insider control problems}, i.e. optimal control
problems of stochastic systems where the controller at any time in addition
to knowledge about the history of the system up to this time, also has
additional information related to a \emph{future} value of the system. Since
this puts the associated controlled systems outside the context of
semimartingales, we apply anticipative white noise analysis, including forward
integration and Hida-Malliavin calculus to study the problem. Combining this
with Donsker delta functionals we transform the insider control problem into a
classical (but parametrised) adapted control system, albeit with a
non-classical performance functional. We establish a sufficient and a necessary
maximum principle for such systems. Then we apply the results to obtain
explicit solutions for some optimal insider portfolio problems in financial
markets described by It\^ o-L\' evy processes. Finally, in the Appendix we give
a brief survey of the concepts and results we need from the theory of white
noise, forward integrals and Hida-Malliavin calculus
Optimal insider control of stochastic partial differential equations
We study the problem of optimal inside control of an SPDE (a stochastic
evolution equation) driven by a Brownian motion and a Poisson random measure.
Our optimal control problem is new in two ways: (i) The controller has access
to inside information, i.e. access to information about a future state of the
system, (ii) The integro-differential operator of the SPDE might depend on the
control.
In the first part of the paper, we formulate a sufficient and a necessary
maximum principle for this type of control problem, in two cases: (1) When the
control is allowed to depend both on time t and on the space variable x. (2)
When the control is not allowed to depend on x.
In the second part of the paper, we apply the results above to the problem of
optimal control of an SDE system when the inside controller has only noisy
observations of the state of the system. Using results from nonlinear
filtering, we transform this noisy observation SDE inside control problem into
a full observation SPDE insider control problem.
The results are illustrated by explicit examples
Optimal insider control and semimartingale decompositions under enlargement of filtration
We combine stochastic control methods, white noise analysis and
Hida-Malliavin calculus applied to the Donsker delta functional to obtain new
representations of semimartingale decompositions under enlargement of
filtrations. The results are illustrated by explicit examples
Extra medullar Granulocytic sarcoma: a case report of an exceptional localization
Granulocytic sarcoma is a rare type of tumor composed of extramedullary immature cells. The breast location is very rare; it accounts for less than 8% of cases. The present study reports the case of a 36-year-old female with a medical history of myelodysplastic syndrome. She was referred because of a lump in the left breast. We have diagnosed a case of granulocytic sarcoma of the breast by core biopsy. Histology and immunohistochemistry showed hypercellular smears with immature myeloid cells. The blast cells were myeloperoxidase positive.
The patient underwent a lumpectomy. Five months later, she developed a contralateral recurrence, treated by lumpectomy and radiotherapy. Three years later, she developed a recurrence in the left knee.
We report this case for its rarity and as a note of caution to a physician to consider myeloid sarcoma in the differential diagnosis of a breast lump, to provide the correct diagnosis and avoid incorrect treatment of a curable disease
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