An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility | Zendy

Hao Chang | Zendy; Ximin Rong | Zendy

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An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility

Author(s) -

Hao Chang,

Ximin Rong

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/219397

Subject(s) - stochastic volatility , rendleman–bartter model , interest rate , hamilton–jacobi–bellman equation , bellman equation , mathematics , volatility (finance) , logarithm , stochastic control , short rate model , heston model , econometrics , cox–ingersoll–ross model , stochastic investment model , investment strategy , economics , mathematical optimization , sabr volatility model , optimal control , financial economics , finance , portfolio , mathematical analysis , asset allocation , market liquidity

We are concerned with an investment and consumption problem with stochastic interestrate and stochastic volatility, in which interest rate dynamic is described by the Cox-Ingersoll-Ross (CIR) modeland the volatility of the stock is driven by Heston’s stochastic volatility model. We apply stochastic optimal controltheory to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function and choose power utility andlogarithm utility for our analysis. By using separate variable approach and variable change technique, we obtainthe closed-form expressions of the optimal investment and consumption strategy. A numerical example is givento illustrate our results and to analyze the effect of market parameters on the optimal investment and consumptionstrategies

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