%0 Journal Article
%T Portfolio Selection with Jumps under Regime Switching
%A Lin Zhao
%J International Journal of Stochastic Analysis
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/697257
%X We investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection is proposed and analyzed for a market consisting of one bank account and multiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. A Markov chain modulated diffusion formulation is employed to model the problem. 1. Introduction The jump diffusion process has come to play an important role in many branches of science and industry. In their book [1], £¿ksendal and Sulem have studied the optimal control, optimal stopping, and impulse control for jump diffusion processes. In mathematical finance theory, many researchers have developed option pricing theory, for example, Merton [2] was the first to use the jump processes to describe the stock dynamics, and Bardhan and Chao [3] were amongst the first authors to consider market completeness in a discontinuous model. The jump diffusion models have been discussed by Chan [4], F£¿llmer and Schweizer [5], El Karoui and Quenez [6], Henderson and Hobson [7], and Merculio and Runggaldier [8], to name a few. On the other hand, regime-switching models have been widely used for price processes of risky assets. For example, in [9] the optimal stopping problem for the perpetual American put has been considered, and the finite expiry American put and barrier options have been priced. The asset allocation has been discussed in [10], and Elliott et al. [11] have investigated volatility problems. Regime-switching models with a Markov-modulated asset have already been applied to option pricing in [12¨C14] and references therein. Moreover, Markowitz's mean-variance portfolio selection with regime switching has been studied by Yin and Zhou [15], Zhou and Yin [16], and Zhou and Li [17]. Portfolio selection is an important topic in finance; multiperiod mean-variance portfolio selection has been studied by, for example, Samuelson [18], Hakansson [19], and Pliska [20] among others. Continuous-time mean-variance hedging problems were attacked by Duffie and Richardson [21] and Schweizer [22] where optimal dynamic strategies were derived, based on the projection theorem, to hedge contingent claims in incomplete markets. In this paper, we will extend the results of Yin and Zhou [15] to SDEs with jumps under regime switching. After dealing with the difficulty from the jump processes, we obtain similar results to those of Yin and Zhou [15]. 2. SDEs under Regime Switching with Jumps Throughout this paper, let be a fixed complete
%U http://www.hindawi.com/journals/ijsa/2010/697257/