Robust non-zero-sum stochastic differential portfolio games with two interacting agents under the Heston model
The stochastic differential portfolio game between two competing investors with undertaking of the relative performance concerns is studied.Assume that the financial market is composed of a risk-free asset and a risky asset whose price process is described by the classical Heston model.Under the framework of Nash equilibrium theory,a non-zero-sum stochastic differential portfolio game model is constructed which maximizes the expected utility of the terminal relative performance.Utilizing the dynamic programming principle,explicit expressions of the value functions and Nash equilibrium for portfolio decisions are obtained under the representative case the CRRA utility.Finally,some numerical examples are performed to illustrate the influence of model parameters on the Nash equilibrium together with some economic interpretations.Results show that,the best response of each investor to the competition is to mimic the strategy of its opponent.Consequently,the portfolio decision of an investor with the relative performance concern is more risky than that without the relative performance concern,and thus increases the systemic risk in financial markets.Moreover,model uncertainty will cause an risk-averse investor to adopt more conservative investment strategies than an ambiguity-neutral investor,which is reflected in the reduction of the amount invested in the risky asset.
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