The Optimal Consumption, Investment and Life Insurance for Wage Earners under Inside Information and Inflation

This paper studies the dynamically optimal consumption, investment and life-insurance strategies for a wage earners under inside information and inflation. Assume that the wage earner can invest in a risk-free asset, a risky asset and an inflation-indexed bond and that the wage earner can obtain some additional information on the risky asset from the financial market. By maximizing the expected utility of the wage earner's consumption, inheritance and terminal wealth, we obtain the dynamically optimal consumption, investment and life-insurance strategies for the wage earner. The method of this paper is mainly based on (dynamical) stochastic control theory and the technique of enlargement of filtrations. Moreover, sensitivity analysis is carried out, which reveals that a wage earner with inside information tends to increase his/her consumption and investment, while reducing his/her purchase of life insurance.