In this paper, we study the optimal portfolio selection problem for weakly informed traders in the sense of Baudoin [1]. Apart from expected utility maximizers, we consider investors with other preference paradigms. In particular, we consider agents following cumulative prospect theory as developed by Tversky and Kahneman [12] as well as Yaari's dual theory of choice [13]. We solve the corresponding optimization problems, in both non-informed and informed case, i.e. when the agent has an additional weak information. Finally, comparison results among investors with different preferences and information sets are given, together with explicit examples. In particular, the insider's gain, i.e. the difference between the optimal values of an informed and a non informed investor, is explicitly computed.
We consider a single-period nancial market model with normally distributed returns and the presence of heterogeneous agents. Specically, some investors are classical Expected Utility maximizers whereas some others follow Cumulative Prospect Theory. Using well-known functional forms for the preferences, we analytically prove that a Security Market Line Theorem holds. This implies that Capital Asset Pricing Model is a necessary (though not sucient) requirement in equilibria with positive prices. We correct some erroneous results about existence of equilibria with Cumulative Prospect Theory investors which had appeared in the last few years and we give sucient conditions for an equilibrium to exist. To circumvent the complexity arising from the interaction of heterogeneous agents, we propose a segmented-market equilibrium model where segmentation is endogenously determined.
This note identifies and fixes a minor gap in Proposition 1 in Barberis and Huang (Am Econ Rev 98(5):2066-2100, 2008. Assuming homogeneous cumulative prospect theory decision makers, we show that CAPM is a necessary (though not sufficient) condition that must hold in equilibrium. We support our results with numerical examples where security prices become negative.
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