Parameter identification for portfolio optimization with a slow stochastic factor. (English) Zbl 1502.35175
Summary: In this paper, we intend to identify two significant parameters – expected return and absolute risk aversion – in the Merton portfolio optimization problem under an exponential utility function where volatility is driven by a slow mean-reverting diffusion process. First, we find the approximate solution of the fully nonlinear Hamilton-Jacobi-Bellman equation for the Merton model by the stochastic asymptotic approximation method. Second, we estimate parameters – expected return and absolute risk aversion – through the approximate solution and prove the uniqueness and stability of the parameter identification problem. Finally, we provide an illustrative example to demonstrate the capacity and efficiency of our method.
MSC:
| 35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |
| 35R30 | Inverse problems for PDEs |
| 60J65 | Brownian motion |
| 65C05 | Monte Carlo methods |
| 91G10 | Portfolio theory |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 93E20 | Optimal stochastic control |
| 35B35 | Stability in context of PDEs |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
portfolio optimization; slow stochastic factor; asymptotic approximation; parameter identification problem; inverse problemsReferences:
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