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.