Under mean-variance-utility framework, we propose a new portfolio selection model, which allows wealth and time both have influences on risk aversion in the process of investment. We solved the model under a game theoretic framework and analytically derived the equilibrium investment (consumption) policy. The results conform with the facts that optimal investment strategy heavily depends on the investors wealth and future income-consumption balance as well as the continuous optimally consumption process is highly dependent on the consumption preference of the investor.
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