Browsing by Author "Ranya Hamid El Nour"

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    An Optimal Consumption Problem in an Incomplete Market
    (Graduate College, 2019-05-15) Ranya Hamid El Nour
    In this paper, the problem of finding the optimal consumption rate is studied. In this problem, the driving process of the controlled (wealth) process is assumed to be Levy. The method adopted in this paper, to find the optimal consumption rate, is the Maximum principle combined with the celebrated Clark-Ocone theorem, which needs the existence Malliavin derivatives and their extension in L^2 spaces. المستخلص: في هذه الورقة دُرست مسألة ايجاد معدل الاستهلاك الأمثل. اعتُبرت، في هذه الورقة، أن العملية العشوائية التي تقود العملية المراد التحكم بها- و التي تمثل ثروة مستثمر ما- هي عملية ليفي. استُخدمت لحل هذه المسألة- من طرق التحكم العشوائي- مبدأ الحد الأعلى مع مساعدة من مبرهنة كلارك-أوكون المعروفة. استخدام مبرهنة كلارك-أوكون يتطلب وجود المشتقات العشوائية أو ما يعرف بمشتقات ماليافين وتمديدها لفضاءات L^2 .
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    Some Harvesting Problems
    (Alneelain University, 2015-07) Ranya Hamid El Nour
    ABSTRACT. The aim of this thesis is to study and solve optimal control problems for systems driven by both: Brownian motion and Levy processes. The methods of solution used are: Dynamic programming, and Maximum principle where the known Clark-Ocone theorem is applied. The application of Clark-Ocone theorem needs the existence of Malliavin derivative and its extesion in L2 spaces. As an application , the thesis considered an example of harvesting problem in a crowded media as well as searching for optimal portfolio strategies in hedging options in markets driven by both: Brovmian motion and Levy processes.