PDE Approach to Exponential Utility Problem Sample Clauses

PDE Approach to Exponential Utility Problem. Here, we would like to solve the exponential utility problem via stochastic control approach. Starting from initial value x, the value process can be described as J(t, x) = ess sup E U x + π T ∫ πudSu t Ft ∫ which seeks the maximal utility over all πt in the time horizon [t, T ]. Consider any possible trading strategy π, assume the above supremum is obtained by some strategy πˆ. For 0 ≤ s ≤ t ≤ T , it follows that ∫ T E[J(t, Xπ)|Fs] = E[E[U (Xπ + πˆudSu)|Ft]|Fs] ∫ t t = E[E[U (Xπ + s ≤ E[E[U (Xπ + s = J(s, Xπ), t t πudSu + ∫ s t πˆudSu + s T ∫ πˆudSu)|Ft]|Fs] t T πˆudSu)|Ft]|Fs] t t t which shows that he value process J(t, Xπ) is a martingale and is a supermartingale under πˆ. Hence, by the martingale optimality principle (lemma 2.2.2.1.), the equality holds for the optimal trading strategy πˆ. By the Ito˜ formula, we can differentiate the value function J(t, Xπ) as dJ(t, Xπ) = (J + µJ π S + 1 σ2J (π S )2)dt + σJ π S dW .
Sample 1
AutoNDA by SimpleDocs

Related to PDE Approach to Exponential Utility Problem

  • Local Utility Services XOOM is an independent retail marketer of natural gas and is not affiliated with your local utility. Your local utility will continue to deliver your natural gas, read your meter, send your bill, and make necessary repairs. Your local utility will also respond to emergencies and provide other basic utility services as required. XOOM is not an agent of your local utility and your utility will not be liable for any of XOOM’s acts, omissions, or representations.

  • PROPOSED MOBILITY PROGRAMME The proposed mobility programme includes the indicative start and end months of the agreed study programme that the student will carry out abroad. The Learning Agreement must include all the educational components to be carried out by the student at the receiving institution (in table A) and it must contain as well the group of educational components that will be replaced in his/her degree by the sending institution (in table B) upon successful completion of the study programme abroad. Additional rows can be added as needed to tables A and B. Additional columns can also be added, for example, to specify the study cycle-level of the educational component. The presentation of this document may also be adapted by the institutions according to their specific needs. However, in every case, the two tables A and B must be kept separated, i.e. they cannot be merged. The objective is to make clear that there needs to be no one to one correspondence between the courses followed abroad and the ones replaced at the sending institutions. The aim is rather that a group of learning outcomes achieved abroad replaces a group of learning outcomes at the sending institution, without having a one to one correspondence between particular modules or courses. A normal academic year of full-time study is normally made up of educational components totalling 60 ECTS* credits. It is recommended that for mobility periods shorter than a full academic year, the educational components selected should equate to a roughly proportionate number of credits. In case the student follows additional educational components beyond those required for his/her degree programme, these additional credits must also be listed in the study programme outlined in table A. When mobility windows are embedded in the curriculum, it will be enough to fill in table B with a single line as described below: Component code (if any) Component title (as indicated in the course catalogue) at the sending institution Semester [autumn / spring] [or term] Number of ECTS* credits Mobility window … Total: 30 Otherwise, the group of components will be included in Table B as follows: Component code (if any) Component title (as indicated in the course catalogue) at the sending institution Semester [autumn / spring] [or term] Number of ECTS* credits Course x … 10 Module y … 10 Laboratory work … 10 Total: 30 The sending institution must fully recognise the number of ECTS* credits contained in table A if there are no changes to the study programme abroad and the student successfully completes it. Any exception to this rule should be clearly stated in an annex of the Learning Agreement and agreed by all parties. Example of justification for non-recognition: the student has already accumulated the number of credits required for his/her degree and does not need some of the credits gained abroad. Since the recognition will be granted to a group of components and it does not need to be based on a one to one correspondence between single educational components, the sending institution must foresee which provisions will apply if the student does not successfully complete some of the educational components from his study programme abroad. A web link towards these provisions should be provided in the Learning Agreement. The student will commit to reach a certain level of language competence in the main language of instruction by the start of the study period. The level of the student will be assessed after his/her selection with the Erasmus+ online assessment tool when available (the results will be sent to the sending institution) or else by any other mean to be decided by the sending institution. A recommended level has been agreed between the sending and receiving institutions in the inter-institutional agreement. In case the student would not already have this level when he/she signs the Learning Agreement, he/she commits to reach it with the support to be provided by the sending or receiving institution (either with courses that can be funded by the organisational support grant or with the Erasmus+ online tutored courses). All parties must sign the document; however, it is not compulsory to circulate papers with original signatures, scanned copies of signatures or digital signatures may be accepted, depending on the national legislation. * In countries where the "ECTS" system it is not in place, in particular for institutions located in partner countries not participating in the Bologna process, "ECTS" needs to be replaced in all tables by the name of the equivalent system that is used and a weblink to an explanation to the system should be added. CHANGES TO THE ORIGINAL LEARNING AGREEMENT The section to be completed during the mobility is needed only if changes have to be introduced into the original Learning Agreement. In that case, the section to be completed before the mobility should be kept unchanged and changes should be described in this section. Changes to the mobility study programme should be exceptional, as the three parties have already agreed on a group of educational components that will be taken abroad, in the light of the course catalogue that the receiving institution has committed to publish well in advance of the mobility periods and to update regularly as ECHE holder. However, introducing changes might be unavoidable due to, for example, timetable conflicts. Other reasons for a change can be the request for an extension of the duration of the mobility programme abroad. Such a request can be made by the student at the latest one month before the foreseen end date. These changes to the mobility study programme should be agreed by all parties within four to seven weeks (after the start of each semester). Any party can request changes within the first two to five-week period after regular classes/educational components have started for a given semester. The exact deadline has to be decided by the institutions. The shorter the planned mobility period, the shorter should be the window for changes. All these changes have to be agreed by the three parties within a two-week period following the request. In case of changes due to an extension of the duration of the mobility period, changes should be made as timely as possible as well. Changes to the study programme abroad should be listed in table C and, once they are agreed by all parties, the sending institution commits to fully recognise the number of ECTS credits as presented in table C. Any exception to this rule should be documented in an annex of the Learning Agreement and agreed by all parties. Only if the changes described in table C affect the group of educational components in the student's degree (table B) that will be replaced at the sending institution upon successful completion of the study programme abroad, a revised version should be inserted and labelled as "Table D: Revised group of educational components in the student's degree that will be replaced at sending institution". Additional rows and columns can be added as needed to tables C and D. All parties must confirm that the proposed amendments to the Learning Agreement are approved. For this specific section, original or scanned signatures are not mandatory and an approval by email may be enough. The procedure has to be decided by the sending institution, depending on the national legislation.

  • Building Commissioning Services The Owner may provide as a part of its testing services the Building Commissioning services involving the project’s HVAC and exhaust systems, temperature control systems, fire detection and alarm systems, emergency power and lighting system, fire suppression system, security locks and security locking control systems, food service equipment (if applicable), and laundry equipment (if applicable). In the event the Using Agency’s Program specifies additional commissioning services, the Owner shall procure such services as well. The Owner, through its Executive Administrator, may engage an independent Commissioning Authority. It is the intent of this Article that the Commissioning Authority enforce the requirements mentioned herein and certify that the systems and equipment listed all function properly prior to the initiation of each final inspection.

  • Access Toll Connecting Trunk Group Architecture 9.2.1 If CBB chooses to subtend a Verizon access Tandem, CBB’s NPA/NXX must be assigned by CBB to subtend the same Verizon access Tandem that a Verizon NPA/NXX serving the same Rate Center Area subtends as identified in the LERG.

  • Network Resource Interconnection Service (check if selected)

  • Network Interconnection Architecture Each Party will plan, design, construct and maintain the facilities within their respective systems as are necessary and proper for the provision of traffic covered by this Agreement. These facilities include but are not limited to, a sufficient number of trunks to the point of interconnection with the tandem company, and sufficient interoffice and interexchange facilities and trunks between its own central offices to adequately handle traffic between all central offices within the service areas at P.01 grade of service or better. The provisioning and engineering of such services and facilities will comply with generally accepted industry methods and practices, and will observe the rules and regulations of the lawfully established tariffs applicable to the services provided.

  • Updated Information Submission by Interconnection Customer The updated information submission by the Interconnection Customer, including manufacturer information, shall occur no later than one hundred eighty (180) Calendar Days prior to the Trial Operation. The Interconnection Customer shall submit a completed copy of the Electric Generating Unit data requirements contained in Appendix 1 to the LGIP. It shall also include any additional information provided to the Participating TO and the CAISO for the Interconnection Studies. Information in this submission shall be the most current Electric Generating Unit design or expected performance data. Information submitted for stability models shall be compatible with the Participating TO and CAISO standard models. If there is no compatible model, the Interconnection Customer will work with a consultant mutually agreed to by the Parties to develop and supply a standard model and associated information. If the Interconnection Customer's data is materially different from what was originally provided to the Participating TO and the CAISO for the Interconnection Studies, then the Participating TO and the CAISO will conduct appropriate studies pursuant to the LGIP to determine the impact on the Participating TO’s Transmission System and affected portions of the CAISO Controlled Grid based on the actual data submitted pursuant to this Article 24.3. The Interconnection Customer shall not begin Trial Operation until such studies are completed and all other requirements of this LGIA are satisfied.

  • Scope of Interconnection Service 1.3.1 The NYISO will provide Energy Resource Interconnection Service to Interconnection Customer at the Point of Interconnection.

  • Interconnection Customer Drawings Within one hundred twenty (120) days after the date of Initial Operation, unless the Interconnection Parties agree on another mutually acceptable deadline, the Interconnection Customer shall deliver to the Transmission Provider and the Interconnected Transmission Owner final, “as-built” drawings, information and documents regarding the Customer Interconnection Facilities, including, as and to the extent applicable: a one-line diagram, a site plan showing the Customer Facility and the Customer Interconnection Facilities, plan and elevation drawings showing the layout of the Customer Interconnection Facilities, a relay functional diagram, relaying AC and DC schematic wiring diagrams and relay settings for all facilities associated with the Interconnection Customer's step-up transformers, the facilities connecting the Customer Facility to the step-up transformers and the Customer Interconnection Facilities, and the impedances (determined by factory tests) for the associated step-up transformers and the Customer Facility. As applicable, the Interconnection Customer shall provide Transmission Provider and the Interconnected Transmission Owner specifications for the excitation system, automatic voltage regulator, Customer Facility control and protection settings, transformer tap settings, and communications.

  • Loop Provisioning Involving Integrated Digital Loop Carriers 2.6.1 Where InterGlobe has requested an Unbundled Loop and BellSouth uses IDLC systems to provide the local service to the End User and BellSouth has a suitable alternate facility available, BellSouth will make such alternative facilities available to InterGlobe. If a suitable alternative facility is not available, then to the extent it is technically feasible, BellSouth will implement one of the following alternative arrangements for InterGlobe (e.g. hairpinning):

Time is Money Join Law Insider Premium to draft better contracts faster.