In this paper we present a theory of health investment when there are multiple causes of death. Since there are several risks competing for one's life, the health investments in avoiding different causes of death are not independent in general. We analyze the optimal investment rules and the comparative statics. In particular, we search for the conditions that make such health investments normal goods, non-Giffen goods, gross complements to one another, and have a positive risk aversion effect. If the proposed conditions fail, then some health investments may become net substitutes, or even gross substitutes to one another.
competing risks complementarity quantity and quality of life and dominant diagonal matrix