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Optimal portfolio selection of mean-variance utility with stochastic interest rate. (English) Zbl 1457.91347

Summary: In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the optimal control over the financial system involving stochastic interest rate and state-dependent risk aversion (SDRA) mean-variance utility. By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. Finally, the numerical examples provided are used to analyze how stochastic (short-term) interest rates and risk aversion affect the optimal control strategies to illustrate the validity of our results.

MSC:

91G10 Portfolio theory
91G30 Interest rates, asset pricing, etc. (stochastic models)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91B16 Utility theory
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