Two-stage optimal control models are a useful tool to model stochastic shocks, which have the potential to significantly alter the characteristics of a dynamic system, but cannot be controlled by the decision maker. Applications can be found in a wide range of topics including health and environmental economics. The Julia package recently received and update to version v0.2.0.

Methods to solve this type of model were limited in the past and were either based substantially simplifying assumptions or required extensive computational efforts. A newly developed transformation technique by Wrzaczek, Kuhn and Frankovic (2021) simplifies this process by transforming the stochastic two-stage-model into an equivalent age-structured optimal control model. This not only leads to more detailed analytical insights, but also allows the usage of established numerical solution methods to solve this class of problems.

We implemented an algorithm based on the works of Veliov (2003) in the Julia Programming Language, which is able to solve two-stage optimal control problem based on just entering the system dynamics and objective. The program code is available upon request and is planned to be released as an open-source toolbox by the start of 2023.

Optimal consumption before and after cancer diagnosis

Health shocks on the household level

Most models on the life-cycle utilization of health care consider the expected development of an individual’s health. However, health shocks with significant impact (e.g. the onset of a chronic disease or life-threatening accidents) should not be averaged, as they can put the life-course onto a different trajectory. This model introduces a dynamic optimal-control framework incorporating a stochastic health shock with individuals allocating their resources to consumption and various types of health care over their life-cycle.

Optimal Lockdown Strategy

Should the COVID-19 lockdown be relaxed or intensified in case a vaccine becomes available?

During the beginning of the pandemic implementing a long-term optimal strategy was not possible since a forecast when R&D will succeed in developing an effective vaccination was not available. Our work closes this gap by assuming a stochastic arrival rate of the COVID-19 vaccine with the corresponding change in the optimal policy regarding the accompanying optimal lockdown measures.

Diagram of DICE model

How to prepare for and adapt to a climate tipping point

In other work YSSP-student Maddalena Muttoni introduced stochastic tipping points into the DICE model during her time at the Economic Frontiers Program in the summer of 2022. Using the 2SOCS model she investigate the various impacts of qualitatively different type of tipping points.

Assessing resilience in a framework of stochastic switches and Skiba points

Project in progress.

Defining Value of Information in a stochastic shock setting

Project in progress.