Abstract:  In this study we investigate a general continuous-time portfolio selection model with loss aversion in an incomplete market where the number of stocks is strictly less than the dimension of the underlying Brownian motion. The investor's preference facing market risks is defined by a S-shaped value function. By transforming the market into a complete one, we solve the optimal terminal wealth and the optimal wealth-portfolio pair of agents using  martingale method and  replicating technique. A special example with a two-piece power function and deterministic coefficients is presented to illustrate the general results. Last, the explicit expressions of the optimal solutions are given.

Key words: loss aversion, portfolio selection, incomplete market, martingale