Consumption and portfolio optimization solvable problems with recursive preferences
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916542400167936 |
|---|---|
| author | Kang, Jian-hao Gou, Zhun Huang, Nan-jing |
| author_facet | Kang, Jian-hao Gou, Zhun Huang, Nan-jing |
| contents | This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general stochastic volatility process. By using Bellman's dynamic programming principle, the Hamilton-Jacobi-Bellman (HJB) equation is derived for characterizing the optimal consumption-investment strategy and the corresponding value function. Based on the conjecture of the exponential-polynomial form of the value function, we prove that, when the order of the polynomial $n\leq2$, the HJB equation has an analytical solution if the investor with unit elasticity of intertemporal substitution (EIS) and an approximate solution otherwise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16365 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Consumption and portfolio optimization solvable problems with recursive preferences Kang, Jian-hao Gou, Zhun Huang, Nan-jing Optimization and Control This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general stochastic volatility process. By using Bellman's dynamic programming principle, the Hamilton-Jacobi-Bellman (HJB) equation is derived for characterizing the optimal consumption-investment strategy and the corresponding value function. Based on the conjecture of the exponential-polynomial form of the value function, we prove that, when the order of the polynomial $n\leq2$, the HJB equation has an analytical solution if the investor with unit elasticity of intertemporal substitution (EIS) and an approximate solution otherwise. |
| title | Consumption and portfolio optimization solvable problems with recursive preferences |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2307.16365 |