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R. C. Merton, “Optimum Consumption and Portfolio Rules in a Continuous-time Model,” Journal of Economic Theory, Vol. 3, No. 4, 1971, pp. 373-413. doi:10.1016/0022-0531(71)90038-X

has been cited by the following article:

• TITLE: An Optimal Life Insurance Policy in the Continuous-Time Investment-Consumption Problem

  AUTHORS: Hideki Iwaki, Yusuke Osaki

  KEYWORDS: Life Insurance; Investment/Consumption Model; Martingale; Convex Duality

  JOURNAL NAME: Journal of Mathematical Finance, Vol.3 No.2, May 24, 2013

  ABSTRACT: This paper considers an optimal life insurance for a household subject to mortality risk. The household receives wage income continuously, which could be terminated by unexpected premature loss of earning power. In order to hedge the risk of losing income stream, the household enters a life insurance contract. The household may also invest their wealth into a financial market. Therefore, the problem is to determine an optimal insurance/investment/consumption strategy. To reflect a real-life situation better, we consider an incomplete market where the household cannot trade insurance contracts continuously. We provide explicit solutions in a fairly general setup.