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...
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doaj-abe2797dc501461a9d8eb59df7080b732020-11-24T23:41:45ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/219397219397An Investment and Consumption Problem with CIR Interest Rate and Stochastic VolatilityHao Chang0Xi-min Rong1Department of Mathematics, Tianjin Polytechnic University, Binshui West Road 399, 300387 Tianjin, ChinaSchool of Science, Tianjin University, Wei-jin Road 72, 300072 Tianjin, ChinaWe 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.http://dx.doi.org/10.1155/2013/219397 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hao Chang Xi-min Rong |
spellingShingle |
Hao Chang Xi-min Rong An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility Abstract and Applied Analysis |
author_facet |
Hao Chang Xi-min Rong |
author_sort |
Hao Chang |
title |
An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility |
title_short |
An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility |
title_full |
An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility |
title_fullStr |
An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility |
title_full_unstemmed |
An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility |
title_sort |
investment and consumption problem with cir interest rate and stochastic volatility |
publisher |
Hindawi Limited |
series |
Abstract and Applied Analysis |
issn |
1085-3375 1687-0409 |
publishDate |
2013-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2013/219397 |
work_keys_str_mv |
AT haochang aninvestmentandconsumptionproblemwithcirinterestrateandstochasticvolatility AT ximinrong aninvestmentandconsumptionproblemwithcirinterestrateandstochasticvolatility AT haochang investmentandconsumptionproblemwithcirinterestrateandstochasticvolatility AT ximinrong investmentandconsumptionproblemwithcirinterestrateandstochasticvolatility |
_version_ |
1725505548323913728 |