scholarly journals On The Closed Form Strategies of an Investor under the CEV and CIR Processes

2021 ◽  
Vol 7 (1) ◽  
pp. 87-107
Author(s):  
Edikan Akpanibah ◽  
◽  
Bright Osu ◽  
Everestus Eze ◽  
Chidi Okonkwo ◽  
...  
Keyword(s):  
Interest Rate ◽  
Absolute Risk ◽  
Optimal Investment ◽  
Explicit Solutions ◽  
Constant Elasticity ◽  
Risky Assets ◽  
Constant Elasticity Of Variance ◽  
Variable Approach ◽  
Cir Process ◽  
The Interest Rate

In this paper, the explicit solutions of the optimal investment plans of an investor with exponential utility function exhibiting constant absolute risk aversion (CARA) under constant elasticity of variance (CEV) and stochastic interest rate is studied. A portfolio comprising of a risk-free asset modelled by the Cox-Ingersoll-Ross (CIR) process and two risky assets modelled by the CEV process is considered, where the instantaneous volatilities of the two risky assets form a 2 x 2 matrix n = {np,q}2x2 such that nnT is positive definite. Using the power transformation and change of variable approach with asymptotic expansion technique, explicit solutions of the optimal investment plans are found. Moreover, numerical simulations are used to study the effects of the interest rate, elasticity parameter, correlation coefficient and the risk averse coefficient on the optimal investment plans.

scholarly journals An Investor’s Investment Plan with Stochastic Interest Rate under the CEV Model and the Ornstein-Uhlenbeck Process

2021 ◽  
pp. 239-249
Author(s):  
Edikan E. Akpanibah ◽  
Udeme O. Ini
Keyword(s):  
Interest Rate ◽  
Stock Market ◽  
Market Price ◽  
Optimal Investment ◽  
Stochastic Interest Rate ◽  
Cev Model ◽  
Constant Elasticity ◽  
Risky Assets ◽  
Investment Plan ◽  
Stochastic Interest

The aim of this paper is to maximize an investor’s terminal wealth which exhibits constant relative risk aversion (CRRA). Considering the fluctuating nature of the stock market price, it is imperative for investors to study and develop an effective investment plan that considers the volatility of the stock market price and the fluctuation in interest rate. To achieve this, the optimal investment plan for an investor with logarithm utility under constant elasticity of variance (CEV) model in the presence of stochastic interest rate is considered. Also, a portfolio with one risk free asset and two risky assets is considered where the risk free interest rate follows the Ornstein-Uhlenbeck (O-U) process and the two risky assets follow the CEV process. Using the Legendre transformation and dual theory with asymptotic expansion technique, closed form solutions of the optimal investment plans are obtained. Furthermore, the impacts of some sensitive parameters on the optimal investment plans are analyzed numerically. We observed that the optimal investment plan for the three assets give a fluctuation effect, showing that the investor’s behaviour in his investment pattern changes at different time intervals due to some information available in the financial market such as the fluctuations in the risk free interest rate occasioned by the O-U process, appreciation rates of the risky assets prices and the volatility of the stock market price due to changes in the elasticity parameters. Also, the optimal investment plans for the risky assets are directly proportional to the elasticity parameters and inversely proportional to the risk free interest rate and does not depend on the risk averse coefficient. 

scholarly journals DC Pension Plan with Refund of Contributions under Affine Interest Rate Model

2020 ◽  
pp. 1-16
Author(s):  
Udeme O. Ini ◽  
Obinichi C. Mandah ◽  
Edikan E. Akpanibah
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Hjb Equation ◽  
Pension Scheme ◽  
Theoretic Approach ◽  
Rate Model ◽  
Risky Assets ◽  
Investment Plan ◽  
Interest Rate Model ◽  
The Impact

This paper studies the optimal investment plan for a pension scheme with refund of contributions, stochastic salary and affine interest rate model. A modified model which allows for refund of contributions to death members’ families is considered. In this model, the fund managers invest in a risk free (treasury) and two risky assets (stock and zero coupon bond) such that the price of the risky assets are modelled by geometric Brownian motions and the risk free interest rate is of affine structure. Using the game theoretic approach, an extended Hamilton Jacobi Bellman (HJB) equation which is a system of non linear PDE is established. Furthermore, the extended HJB equation is then solved by change of variable and variable separation technique to obtain explicit solutions of the optimal investment plan for the three assets using mean variance utility function. Finally, theoretical analyses of the impact of some sensitive parameters on the optimal investment plan are presented.

Invariant approach to optimal investment-consumption problem: the constant elasticity of variance (CEV) model

2016 ◽  
Vol 40 (5) ◽  
pp. 1382-1395 ◽  
Author(s):  
Ahmet Bakkaloglu ◽  
Taha Aziz ◽  
Aeeman Fatima ◽  
F.M. Mahomed ◽  
Chaudry Masood Khalique
Keyword(s):  
Optimal Investment ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Invariant Approach

Defined contribution pension planning with a stochastic interest rate and mean-reverting returns under the hyperbolic absolute risk aversion preference

2019 ◽  
Author(s):  
Hao Chang ◽  
Chunfeng Wang ◽  
Zhenming Fang ◽  
Dan Ma
Keyword(s):  
Interest Rate ◽  
Absolute Risk ◽  
Market Price ◽  
Optimal Strategies ◽  
Stochastic Interest Rate ◽  
Market Price Of Risk ◽  
Absolute Risk Aversion ◽  
Stochastic Interest ◽  
Price Of Risk ◽  
The Interest Rate

Abstract The interest rate and the market price of risk may be stochastic in a real-world financial market. In this paper, the interest rate is assumed to be driven by a stochastic affine interest rate model and the market price of risk from the stock market is a mean-reverting process. In addition, the dynamics of the stock are simultaneously driven by random sources of interest rate and the stock market itself. In pension fund management, different fund managers may have different risk preferences. We suppose risk preference is described by the hyperbolic absolute risk aversion utility, which is a general utility function describing different risk preferences. Legendre transform-dual theory is presented to successfully obtain explicit expressions for optimal strategies. A numerical example illustrates the sensitivity of optimal strategies to market parameters. Theoretical results imply that the risks from stochastic interest rate and stochastic return may be completely hedged by adopting specific portfolios.

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