 To overcome its path-dependent nature, the consumption running maximum process is chosen as an auxiliary state process that renders the value function two dimensional depending on the wealth variable x and the reference variable h.
<coherence>  To overcome its path-dependent nature, the consumption running maximum process is chosen as an auxiliary state process that renders the value function two dimensional depending on the wealth variable x and the reference variable h.
 The consumption running maximum process is chosen as an auxiliary state process that renders the value function two dimensional depending on the wealth variable x and the reference variable h.