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An Optimal Life Insurance Policy in the Continuous-Time Investment-Consumption Problem
Faculty of Business Administration, Kyoto Sangyo University, Kyoto, Japan
Faculty of Economics, Osaka Sangyo University, Osaka, Japan
- 1 Faculty of Business Administration, Kyoto Sangyo University, Kyoto, Japan
- 2 Faculty of Economics, Osaka Sangyo University, Osaka, Japan
Journal of Mathematical Finance·Volume 03 (2013)·Pages 291–306·Published 24 May 2013·DOI10.4236/jmf.2013.32029
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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 .
KeywordsLife InsuranceInvestment/Consumption ModelMartingaleConvex Duality
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