We study the utility maximisation problem in a continuous time market with regime switching.
The regime does not only enter into the market parameters, but also changes the preference modelled by utility function. With the changing utility function, the utility maximisation problem  is not time consistent. In this paper, we aims at the equilibrium trading strategy defined for  time-inconsistent dynamic decision problem. We find out explicit equilibrium trading strategies  for two types of utility functions. Surprisingly, they happen to be the same as the naive trading  strategies, which are relatively easy to find but lack of  justification in general.

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