Exponential utility with non-negative consumption

Details Exponential utility with non-negative consumption Exponential utility with non-negative consumption

2011-06-15

arxiv.org/abs/1106.3006v2

Economy

Quantitative Finance

Portfolio Management

Submitted

Scientific paper

This paper investigates various aspects of the discrete-time exponential utility maximization problem, where feasible consumption policies are not permitted to be negative. By using the Kuhn-Tucker theorem, some ideas from convex analysis and the notion of aggregate state price density, we provide a solution to this problem, in the setting of both complete and incomplete markets (with random endowments). Then, we exploit this result and use certain fixed-point techniques to provide an explicit characterization of a heterogeneous equilibrium in a complete market setting. Moreover, we construct concrete examples of models admitting multiple (including infinitely many) equilibria. By using Cramer's large deviation theorem, we study the asymptotic behavior of endogenously determined in equilibrium prices of zero coupon bonds. Lastly, we show that for incomplete markets, un-insurable future income reduces the current consumption level, thus confirming the presence of the precautionary savings motive in our model.

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