Abstract
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.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11871435
Award Identifier / Grant number: 11471287
Funding statement: This work was supported by the National Natural Science Foundation of China with grant no. 11871435 and 11471287.
A The accuracy of the approximation for 𝜑
The linear PDE (2.15) is rewritten as
where ℳ is defined in (2.5), and we define
where
With this choice of functions
where the source term
Denoting by
Under our assumptions, one sees by direct computation that
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Parameter identification for portfolio optimization with a slow stochastic factor
- Simultaneous inversion of a fractional order and a space source term in an anomalous diffusion model
- On the inverse gravimetry problem with minimal data
- On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission
- Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems
- Convergence analysis of iteratively regularized Gauss–Newton method with frozen derivative in Banach spaces
- Identification of an unknown flexural rigidity of a cantilever Euler–Bernoulli beam from measured boundary deflection
- Hadamard’s example and solvability of the mixed Cauchy problem for the multidimensional Gellerstedt equation
- Ill-posed problems and the conjugate gradient method: Optimal convergence rates in the presence of discretization and modelling errors
- Simultaneous determination of mass density and flexural rigidity of the damped Euler–Bernoulli beam from two boundary measured outputs
Artikel in diesem Heft
- Frontmatter
- Parameter identification for portfolio optimization with a slow stochastic factor
- Simultaneous inversion of a fractional order and a space source term in an anomalous diffusion model
- On the inverse gravimetry problem with minimal data
- On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission
- Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems
- Convergence analysis of iteratively regularized Gauss–Newton method with frozen derivative in Banach spaces
- Identification of an unknown flexural rigidity of a cantilever Euler–Bernoulli beam from measured boundary deflection
- Hadamard’s example and solvability of the mixed Cauchy problem for the multidimensional Gellerstedt equation
- Ill-posed problems and the conjugate gradient method: Optimal convergence rates in the presence of discretization and modelling errors
- Simultaneous determination of mass density and flexural rigidity of the damped Euler–Bernoulli beam from two boundary measured outputs