Before revision:  We derive an explicit formula for the optimal consumption policies involving a put option depending on the state price density . We exploit this formula to prove the existence of an equilibrium and then provide a characterization of all possible equilibria, under the assumption of positive endowments. Via particular examples, we demonstrate that uniqueness is not always guaranteed. Finally, we discover the presence of infinitely many equilibria when endowments are vanishing .
After revision:  We derive an explicit formula for the optimal consumption policies involving a put option depending on the 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 .