# American Institute of Mathematical Sciences

## Explicit investment setting in a Kaldor macroeconomic model with macro shock

 1 School of Mathematics, South China University of Technology, Guangzhou, 510640, China 2 Guangzhou International Institute of Finance and Guangzhou University, Guangzhou, 510405, China

* Corresponding author: Shuanglian Chen

Received  July 2018 Revised  December 2018

Fund Project: The work is supported by the National Natural Science Foundation (No.11701115) and Postdoctoral Science Foundation (No.2017610515)

As the inevitable attributes of macro shocks on macroeconomic system, in this paper, we develop a Kaldor macroeconomic model with shock. The shock is due to the investment uncertainty. We then provide an approach for macroeconomic control by calibrating the evolvement of the shocked Kaldor macroeconomic model with some expected benchmark process. The calibration is realized through the setting for investment. The benchmark process is usually the reflection of decisions or policies. An optimal investment setting associated with a five-dimensional nonlinear system of ordinary differential equations is presented. Through a logical modification for the boundary conditions, the nonlinear system is simplified to be linear and a completely explicit formula for the optimal investment setting is achieved. The rationality of the modification is supported by some stability condition. To cope with the systematic risk caused by the macro shock, we define a dynamic Value-at-Risk(VaR) as the risk measure capturing the risk level of the shocked Kaldor macroeconomic model and introduce a risk constraint into the programming of calibration. Then a constrained investment setting is presented. Finally, we carry out an application of the theoretical results by calibrating the evolvement of the shocked Kaldor macroeconomic model with the business cycle generated from the classical Kaldor model through the investment setting.

Citation: Zhenzhen Wang, Zhenghui Li, Shuanglian Chen, Zhehao Huang. Explicit investment setting in a Kaldor macroeconomic model with macro shock. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020093
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##### References:
Evolvement of the gross production $Y$. The blue line depicts the evolvement in the shocked Kaldor model without calibration and the red line depicts the cycle fluctuation. The intensity of shock is set as $\epsilon = 0.5$
Evolvement of the gross production $Y$. The blue line depicts the evolvement in the shocked Kaldor model without calibration and the red line depicts the cycle fluctuation. The intensity of shock is set as $\epsilon = 2$
Evolvement of the gross production $Y$. The blue line depicts the calibrated evolvement in the shocked Kaldor model and the red line depicts the cycle fluctuation. The intensity of shock is set as $\epsilon = 0.5$
Evolvement of the gross production $Y$. The blue line depicts the calibrated evolvement in the shocked Kaldor model and the red line depicts the cycle fluctuation. The intensity of shock is set as $\epsilon = 2$
Evolvement of the gross production $Y$. The green line depicts the calibrated evolvement in the shocked Kaldor model with risk constraint and the blue line depicts the one without risk constraint. The intensity of shock is set as $\epsilon = 0.5$
Evolvement of the gross production $Y$. The green line depicts the calibrated evolvement in the shocked Kaldor model with risk constraint and the blue line depicts the one without risk constraint. The intensity of shock is set as $\epsilon = 2$
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