Portfolio Strategy of Financial Market with Regime Switching Driven by Geometric Lévy Process

Abstract

The problem of a portfolio strategy for financial market with regime switching driven by geometric Lévy process is investigated in this paper. The considered financial market includes one bond and multiple stocks which has few researches up to now. A new and general Black-Scholes (B-S) model is set up, in which the interest rate of the bond, the rate of return, and the volatility of the stocks vary as the market states switching and the stock prices are driven by geometric Lévy process. For the general B-S model of the financial market, a portfolio strategy which is determined by a partial differential equation (PDE) of parabolic type is given by using Itô formula. The PDE is an extension of existing result. The solvability of the PDE is researched by making use of variables transformation. An application of the solvability of the PDE on the European options with the final data is given finally.