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In this paper we study the dual control approach for the optimal asset allocation problem in a continuous-time regime-switching market. We find the lower and upper bounds of the value function that is a solution to a system of fully coupled nonlinear partial differential equations. These bounds can be tightened with additional controls to the dual process. We suggest a Monte-Carlo algorithm for computing the tight lower and upper bounds and show the method is effective with a variety of utilitydoi:10.1016/j.ejor.2017.04.056 fatcat:r6g2qd2vcfharn5dt2ykj3u6sm