In the general equilibrium with incomplete asset markets (GEI) model, the excess demand functions are typically not continuous at the prices for which the assets have redundant returns. The reason is that, at these prices, the return matrix drops rank and households’ budget sets collapse suddenly. This discontinuity results in a serious problem for the existence and computation of general equilibrium. In this paper, we show that this problem can be resolved with a new return matrix, which has constant rank. As a function of the price vector, the continuity of this new return matrix is ensured on a subset of the price space. This enables us to handle incomplete markets using a standard homotopy path-following argument by restricting the price vector to such a subset. The proposed approach naturally provides a constructive proof for the generic existence of general equilibrium. A homotopy method can then be applied to compute equilibria in the GEI model. Numerical experiments are presented to illustrate its efficiency.

中文翻译：

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不完全市场的光滑同伦方法

在具有不完全资产市场 (GEI) 模型的一般均衡中，超额需求函数通常在资产具有冗余回报的价格上不连续。原因是，在这些价格下，回报矩阵排名下降，家庭预算集突然崩溃。这种不连续性给一般均衡的存在和计算带来了严重的问题。在本文中，我们展示了这个问题可以用一个新的返回矩阵来解决，该矩阵具有恒定的秩。作为价格向量的函数，这个新的回报矩阵的连续性在价格空间的一个子集上得到保证。这使我们能够通过将价格向量限制为这样的子集，使用标准的同伦路径跟随参数来处理不完整市场。所提出的方法自然地为一般均衡的一般存在提供了建设性的证明。然后可以应用同伦方法来计算 GEI 模型中的平衡。给出了数值实验来说明其效率。