Wang Yinuo. Non-Zero Sum Stochastic Differential Investment And Financial Market Game Under Model Uncertainty. Dynamic Systems and Applications 29 (2020) No. 5, 1979 – 1987

https://doi.org/10.46719/dsa202029531

ABSTRACT.
A non-zero and impossible difference game delay. Not only state variables, but also player control variables include delays. This kind of play is encouraged by some new issues of economy and finance. In a Markov environment, the difference between zero and impossibility uncertainty game problems is a constant time shift; the Markov geometric Brownian movement limits the dynamics of risk properties. Market factors, including changing bank interest rates and appreciation and risk assets, are based on the Markov chain change over time. Markov Modified Geometric Brownian Motion (MMGBM) Model Facing Uncertainty Who seeks to worry about non-zero relative performance and impossibility difference game between optimal investment and reinsurance decision. Each MMGBM invests in risky assets and risk-free assets and manages its own risk by reinsuring its opponents and increasing the expected use of the terminal more than the relative of the buyer. Between performance concerns compared to MMGBM and their remaining processes is the impact of insurance companies on the one-on-one impact on index applications. We established an overall framework for the Nash equilibrium, the corresponding non-zero-sum games, and model uncertainty. Numerical studies are based on economic interpretations. The system is based on the MMGBM equation plus economic arguments. The system is a particular case where the Markov chain proposed in two states. Parameters.

Keywords: Markov environment, Modified Geometric Brownian Motion, Nash equilibrium, non-zero-sum games, Markov chain