We investigate the conditions under which life-cycle investment strategies based on age may be ‘near enough' to optimal, focusing on the treatment of the pension account balance and assumptions about risk aversion. We show that dynamically adjusting the strategy in response to fluctuations in...

In a traditional Black-Scholes market we develop a verification theorem for a generalclass of investment and consumption problems where the standard dynamic programmingprinciple does not hold. The theorem is an extension of the standard Hamilton-Jacobi-Bellman equation in the form of a system of...

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 varies with time, having in mind an investor with age-dependent risk...

This paper develops a continuous-time Markov model for utility optimization for households. The household optimizes expected future utility from consumption by controlling consumption, investments and purchase of life insurance on each person in the household. The optimal controls are...

We formalize a consumption-investment-insurance problem with the distinction of a state-dependent relative risk aversion. The state-dependence refers to the state of the finite state Markov chain that also formalizes insurable risks such as health and lifetime uncertainty. We derive and analyze...