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Wealth Martingale and Neighborhood Turnpike Property in Dynamically Complete Market with Heterogeneous Investors

Dai, Darong (2011): Wealth Martingale and Neighborhood Turnpike Property in Dynamically Complete Market with Heterogeneous Investors. Forthcoming in: Economic Research Guardian

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Abstract

In the current paper, a dynamically complete financial market with finite and countable heterogeneous investors has been constructed. Self-dynamic game is defined, that is, the investors determine the optimal bankruptcy time first, and then the optimal portfolio policy. Sub-game perfect Nash equilibrium bankruptcy time is derived and it is confirmed that there exists a unique value of efficient terminal wealth for each investor. The interesting theorem of the current paper proves that the vector of efficient terminal wealth exhibits neighborhood turnpike property if the corresponding optimal path of wealth accumulation is a martingale for each investor. This result would be regarded as an interesting neighborhood turnpike theorem in mathematical finance because it focuses on terminal wealth accumulation of the investors which indeed plays a crucial role in mathematical finance. And it also provides us with an internal\intrinsic and a simple relationship between fairness and efficiency characterizations of the modern financial-market institutions.

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