APPROXIMATE ANALYTICAL SOLUTION TO CONSUMPTION AND LONG-TERM SECURITY INVESTMENT OPTIMIZATION PROBLEM WITH HOMOTHETIC ROBUST UTILITY

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  • 相似拡大的頑健効用投資家の消費と長期証券投資の最適化問題に対する近似解析解
  • ソウジ カクダイテキ ガンケン コウヨウ トウシカ ノ ショウヒ ト チョウキ ショウケン トウシ ノ サイテキカ モンダイ ニ タイスル キンジ カイセキカイ

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Abstract

<p>After the global financial crisis, there has been a growing recognition for the necessity of robust investment optimization which considers Knightian uncertainty, which cannot specify the assumed stochastic process itself. This paper explores the consumption and long-term security investment optimization problem of the investor, who has homothetic robust utility proposed by Maenhout, under generalized security markets including all maturity inflation-indexed bonds, where short-term interest rate and market price of risk depend on state variables. Although a closed-form solution cannot be obtained due to non-linear and non-homogeneous PDE of the value function, an approximate analytical solution is derived applying log-linear approximation of Campbell and Viceira and Kusuda, to the PDE. It is revealed that approximate optimal investment hinges not only on relative risk aversion but also on relative ambiguity aversion to Knightian uncertainty.</p>

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