Riesz representation and optimal stopping with two case studies

Sören Christensen, Paavo Salminen

    Tutkimustuotos: Kirja/lehti/raporttiTutkimusraporttiAmmatillinen


    In this paper we demonstrate that optimal stopping problems can be studied very effectively using as the main tool the Riesz integral representation of excessive functions. After a short general discussion of the Riesz representation we concretize, firstly, on a d-dimensional and, secondly, a space-time one-dimensional geometric Brownian motion. After this, two classical optimal stopping problems are discussed: 1) the optimal investment problem and 2) the valuation of the American put option. It is seen in both of these problems that the boundary of the stopping region can be characterized as a unique solution of an integral equation arising immediately from the Riesz representation of the value function. In Problem 2 the derived equation coincides with the standard well-known equation found in the literature.
    AlkuperäiskieliEi tiedossa
    KustantajaCorenell University Library, arXiv.org > math > arXiv:1309.2469v2
    TilaJulkaistu - 2014
    OKM-julkaisutyyppiD4 Julkaistut kehitykset tai tutkimusraportit tai tutkimukset