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  • 1.
    Agram, Nacira
    et al.
    Department of Mathematics, University of Oslo, Oslo, Norway;Department of Mathematics, Linnaeus University (LNU), Växjö, Sweden.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Oslo, Norway.
    Mean-field stochastic control with elephant memory in finite and infinite time horizon2019In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 91, no 7, p. 1041-1066Article in journal (Refereed)
  • 2.
    Agram, Nacira
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Oslo, Norway.
    The Donsker delta function and local time for McKean–Vlasov processes and applications2023In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, p. 1-18Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is to establish a stochastic differential equation for the Donsker delta measure of the solution of a McKean–Vlasov (mean-field) stochastic differential equation. If the Donsker delta measure is absolutely continuous with respect to Lebesgue measure, then its Radon–Nikodym derivative is called the Donsker delta function. In that case it can be proved that the local time of such a process is simply the integral with respect to time of the Donsker delta function. Therefore we also get an equation for the local time of such a process. For some particular McKean–Vlasov processes, we find explicit expressions for their Donsker delta functions and hence for their local times. 

  • 3.
    Agram, Nacira
    et al.
    Department of Mathematics, University of Oslo, Oslo, Norway;University Mohamed Khider of Biskra, Biskra, Algeria.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Oslo, Norway.
    Yakhlef, Samia
    University Mohamed Khider of Biskra, Biskra, Algeria.
    New approach to optimal control of stochastic Volterra integral equations2018In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 91, no 6, p. 873-894Article in journal (Refereed)
  • 4.
    Djehiche, Boualem
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hamdi, Ali
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    A full balance sheet two-mode optimal switching problem2015In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 87, no 4, p. 604-622Article in journal (Refereed)
    Abstract [en]

    We formulate and solve a finite horizon full balance sheet of a two-mode optimal switching problem related to trade-off strategies between expected profit and cost yields. Given the current mode, this model allows for either a switch to the other mode or termination of the project, and this happens for both sides of the balance sheet. A novelty in this model is that the related obstacles are nonlinear in the underlying yields, whereas, they are linear in the standard optimal switching problem. The optimal switching problem is formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We prove the existence of a continuous minimal solution of this system using an approximation scheme and fully characterize the optimal switching strategy.

  • 5. Nyström, Kaj
    et al.
    Önskog, Thomas
    Remarks on the Skorohod problem and reflected Lévy driven SDEs in time-dependent domains2015In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 87, no 5, p. 747-765Article in journal (Refereed)
    Abstract [en]

    We consider the Skorohod problem for cadlag functions, and the subsequent construction of solutions to normally reflected stochastic differential equations driven by Levy processes, in the setting of non-smooth and time-dependent domains.

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