Abstract
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.
Highlights
Portfolio optimization, which is an important topic in the financial market, has been studied by a vast of researchers after the first publication by Markowitz [1]
The remaining of the article is compiled in the following manner: in Section 2, we explain the setting of the financial market, while the structure is of a mean-variance optimal asset portfolio model with the stochastic interest rate under state-dependent risk aversion (SDRA)
Let the model be composed of two assets being a stock and a bond with the interest rate of the bond being governed by a stochastic process
Summary
Portfolio optimization, which is an important topic in the financial market, has been studied by a vast of researchers after the first publication by Markowitz [1]. Basak and Chabakauri [26], especially, were interested in using the game theory for the continuous portfolio optimization problem The development, both from the modeling and the actual economic meaning, is made by Bjork and Murgoci [27] through extending the analysis to other different objective functions than the mean-variance one. The parameters in the stochastic processes are determined through the classical experimental data For this particular problem, we present the generalized extension of the HJB equation, applying the developed control theory with time inconsistency by Bjork and Murgoci [27]. The remaining of the article is compiled in the following manner: in Section 2, we explain the setting of the financial market, while the structure is of a mean-variance optimal asset portfolio model with the stochastic (short-term) interest rate under state-dependent risk aversion (SDRA).
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