An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility
We are concerned with an investment and consumption problem with stochastic interest rate and stochastic volatility, in which interest rate dynamic is described by the Cox-Ingersoll-Ross (CIR) model and the volatility of the stock is driven by Heston’s stochastic volatility model. We apply stochasti...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/219397 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We are concerned with an investment and consumption problem with stochastic interest
rate and stochastic volatility, in which interest rate dynamic is described by the Cox-Ingersoll-Ross (CIR) model
and the volatility of the stock is driven by Heston’s stochastic volatility model. We apply stochastic optimal control
theory to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function and choose power utility and
logarithm utility for our analysis. By using separate variable approach and variable change technique, we obtain
the closed-form expressions of the optimal investment and consumption strategy. A numerical example is given
to illustrate our results and to analyze the effect of market parameters on the optimal investment and consumption
strategies. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |