Predictable Forward Performance Processes: Infrequent Evaluation and Robo-Advising Applications

We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in the binomial tree model for the financial market. The key step in the construction of these processes is to solve a linear functional equation of higher order associated with the inverse problem driving the evolution of the predictable forward process. We provide sufficient conditions for the existence and uniqueness and an explicit construction of the predictable forward process under these conditions. Furthermore, we show that these processes are time-monotone in the evaluation period. Finally, we argue that predictable forward preferences are a viable framework to model preferences for robo-advising applications and determine an optimal interaction schedule between client and robo-advisor that balances a tradeoff between increasing uncertainty about the client's beliefs on the financial market and an interaction cost.