İkinci mertebeden market hacimli almgren-chriss modelinin özel fonksiyonlar yardımıyla çözümü

One of the current topics of research in mathematical finance is the scheduling of buy or sell orders to liquidate a position. A well-known framework for this problem is the one proposed by Almgren and Chriss that poses the problem as the maximization of the expected utility of the final terminal wealth. In the simplest formulation of the problem the market trading volume is taken as a constant. Under this and other assumptions an optimal trading curve can be computed in terms of the sinh function. This study aims to consider the same model under the assumptions that the market trading volume is an affine function of time, i.e, V_t = at+b and a quadratic function of time i.e, V_t = at^2+bt+c. A solution of the differential equations arising from the Almgren Chriss model under these assumptions is given in terms of the Modified Bessel function (for the affine volume curve) and the confluent hypergeometric function (for the quadratic volume curve). We also provide numerical examples on how the optimal trading curve varies with the model parameters a, b and c.