Multidimensional model of the dynamics of stock prices and the problem of constructing the investment portfolio (Q2760716)

The authors expose a multidimensional model of the dynamics of stock prices based on using the generalized Itô stochastic differential equations. The model suggested is written in the form of a system of stochastic differential equations NEWLINE\[NEWLINE dY(t) = P dt + C dW(t),\qquad Y(0) = Y_0,\qquad 0\leq t\leq T, NEWLINE\]NEWLINE where \(Y(t) = (\ln s_{t1},\ln s_{t2},\dots,\ln s_{tN})\), \(Y_0 = (\ln s_{01},\ln s_{02},\dots, \ln s_{0N})\). Here \(W(\cdot)\) is the \(N\)-dimensional standard Wiener process, \(P\) is the \(N\)-dimensional vector of constant parameters, \(C\) is the nonsingular \(N\times N\)-matrix of constant parameters, \(s_{ti}\) denotes the price of the \(i\)th stock. The authors obtain estimates for the unknown parameters of the model under consideration on the basis of historical prices. The characteristics of risk and profit of the investment portfolio is calculated by the Monte Carlo method that makes it possible to construct the set of permissible portfolios.