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 $t$ 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

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

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

Global weak solutions for some Oldroyd models

We investigate an evolutive system of non-linear partial differential equations derived from Oldroyd models on Non-Newtonian flows. We prove global existence of weak solutions, in the case of a smooth bounded domain, for general initial data. The results hold true for the periodic case.Comment: Submitte