Portfolio with one risk-free and one risky assets was explored in cite{BT1995, LO1999, SS2000, Gomes2005, Bassett2004, DGP2008, BG2009, HZ2009} for risk averse investors. Most of them, for example, cite{BT1995, LO1999, SS2000, Gomes2005, Bassett2004, DGP2008} focus on empirical or numerical studies, except for some optimization problems solved simply by heuristics. Some analytical treatments have been carried out for single period portfolio choice models, and closed-form solutions were obtained for a number of interesting cases, see, for example, cite{BG2009,HZ2009}. Since investors' risk aversion is of first order cite{EZ1990}, known results in cite{Gomes2005} are constraint. Considering investors' general risk aversion, this paper models portfolio with one risk-free and one risky assets for risk averse investors with general value functions, including specific power utility or risk of first order, explores optimal portfolio choice analytically, then interprets equity premium puzzle. Since this paper treats with general value functions including, in particular, ones of constant relative risk aversion, our results generalizes cite{BT1995, LO1999, SS2000, Gomes2005, Bassett2004, BKP2004, DGP2008} on single period portfolio choice.
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