Optimal consumption and investment under time-varying relative risk aversion

Mogens Steffensen (1)

1 Department of Mathematical Sciences

We consider the continuous time consumption-investment problem originally formalized and solved by Merton in case of constant relative risk aversion. We present a complete solution for the case where relative risk aversion with respect to consumption varies with time, having in mind an investor with age-dependent risk aversion. This provides a new motivation for life-cycle investment rules. We study the optimal consumption and investment rules, in particular in the case where the relative risk aversion with respect to consumption is increasing with age.

Mots clés: G11; Merton's problem; Hamilton-Jacobi-Bellman equation; Marginal indirect utility; Life-cycle investment

Domaines: Économie et finance quantitative [q-fin]

Mogens Steffensen. Optimal consumption and investment under time-varying relative risk aversion. Journal of Economic Dynamics and Control, 2011, 35 (5), pp.659. ⟨10.1016/j.jedc.2010.12.007⟩. ⟨hal-00796302⟩