We find the possible risk minimizing portfolio strategies in a two dimensional market consisting of a risk asset and risk-less asset. The investor in the market is subjected to consumption, purchasing of life insurance and stochastic income with inflation risk. The problem is formulated as zero sum game problem between the market and the investor. The strategies are determined for the different generations of the life of an investor, that is before the investor dies and after the investor dies. We used the concept of convex risk measures and monetary utility maximizing problem-concept studied before finding the risk minimizing portfolios which was solved using the game theoretic approach to obtain the strategies explicitly given in the propositions in the study.