scholarly journals Optimal Investment and Consumption Decisions under the Constant Elasticity of Variance Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong ◽  
Hui Zhao ◽  
Chu-bing Zhang
Keyword(s):  
Stock Price ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Power Utility ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Consumption Decisions ◽  
Optimal Investment And Consumption ◽  
Consumption Strategies

We consider an investment and consumption problem under the constant elasticity of variance (CEV) model, which is an extension of the original Merton’s problem. In the proposed model, stock price dynamics is assumed to follow a CEV model and our goal is to maximize the expected discounted utility of consumption and terminal wealth. Firstly, we apply dynamic programming principle to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function. Secondly, we choose power utility and logarithm utility for our analysis and apply variable change technique to obtain the closed-form solutions to the optimal investment and consumption strategies. Finally, we provide a numerical example to illustrate the effect of market parameters on the optimal investment and consumption strategies.

scholarly journals Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Huiling Wu
Keyword(s):  
Regime Switching ◽  
Stock Price ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Power Utility ◽  
Optimal Investment Strategy ◽  
Admissible Strategies ◽  
Definition Of ◽  
Markovian Regime Switching ◽  
Optimal Investment And Consumption

This paper studies an investment-consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous-time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.

scholarly journals Legendre Transform-Dual Solution for a Class of Investment and Consumption Problems with HARA Utility

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Absolute Risk ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Power Utility ◽  
Transform Method ◽  
Intermediate Consumption ◽  
Special Cases ◽  
Hara Utility ◽  
Optimal Investment And Consumption

This paper provides a Legendre transform method to deal with a class of investment and consumption problems, whose objective function is to maximize the expected discount utility of intermediate consumption and terminal wealth in the finite horizon. Assume that risk preference of the investor is described by hyperbolic absolute risk aversion (HARA) utility function, which includes power utility, exponential utility, and logarithm utility as special cases. The optimal investment and consumption strategy for HARA utility is explicitly obtained by applying dynamic programming principle and Legendre transform technique. Some special cases are also discussed.

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

scholarly journals Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Stock Price ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Order Partial Differential Equation ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Time Dynamic ◽  
Mean Variance

This paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV) process. Firstly, we apply Lagrange duality theorem to change an original mean-variance problem into an equivalent optimization one. Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. Finally, the closed-form solutions to the optimal investment strategy and efficient frontier are derived by applying variable change technique.

Estimation in the Constant Elasticity of Variance Model

2001 ◽  
Vol 7 (2) ◽  
pp. 275-292 ◽  
Author(s):  
K.C. Yuen ◽  
H. Yang ◽  
K.L. Chu
Keyword(s):  
Diffusion Process ◽  
Stock Price ◽  
Estimation Procedure ◽  
Stock Option ◽  
Parameter Estimates ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Black Scholes ◽  
Two Parameters

ABSTRACTThe constant elasticity of variance (CEV) diffusion process can be used to model heteroscedasticity in returns of common stocks. In this diffusion process, the volatility is a function of the stock price and involves two parameters. Similar to the Black-Scholes analysis, the equilibrium price of a call option can be obtained for the CEV model. The purpose of this paper is to propose a new estimation procedure for the CEV model. A merit of our method is that no constraints are imposed on the elasticity parameter of the model. In addition, frequent adjustments of the parameter estimates are not required. Simulation studies indicate that the proposed method is suitable for practical use. As an illustration, real examples on the Hong Kong stock option market are carried out. Various aspects of the method are also discussed.

scholarly journals Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xiaotao Liu ◽  
Hailong Liu
Keyword(s):  
Portfolio Choice ◽  
Optimal Investment ◽  
Risk Process ◽  
Cev Model ◽  
Constant Elasticity ◽  
Economic Implications ◽  
Constant Elasticity Of Variance ◽  
Surplus Process ◽  
Hamilton Jacobi Bellman ◽  
Negative Exponential

This paper investigates the optimal portfolio choice problem for a large insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) model. The surplus process is assumed to follow a diffusion approximation model with the Brownian motion in which is correlated with that driving the price of the risky asset. We first derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and then obtain explicit solutions to the value function as well as the optimal control by applying a variable change technique and the Feynman–Kac formula. Finally, we discuss the economic implications of the optimal policy.

scholarly journals Determining Equivalent Administrative Charges for Defined Contribution Pension Plans under CEV Model

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Hongjing Chen ◽  
Zheng Yin ◽  
Tianhao Xie
Keyword(s):  
Pension Plan ◽  
Pension Plans ◽  
Defined Contribution ◽  
Power Utility ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
The Maximum Principle ◽  
Equivalent Equation ◽  
Defined Contribution Pension Plan

In defined contribution pension plan, the determination of the equivalent administrative charges on balance and on flow is investigated if the risk asset follows a constant elasticity of variance (CEV) model. The maximum principle and the stochastic control theory are applied to derive the explicit solutions of the equivalent equation about the charges. Using the power utility function, our conclusion shows that the equivalent charge on balance is related to the charge on flow, risk-free interest rate, and the length of accumulation phase. Moreover, numerical analysis is presented to show our results.

Valuation of American Continuous-Installment Options Under the Constant Elasticity of Variance Model

2016 ◽  
Vol 4 (2) ◽  
pp. 149-168
Author(s):  
Guohe Deng ◽  
Guangming Xue
Keyword(s):  
Closed Form ◽  
Stock Price ◽  
Option Price ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Closed Form Solutions ◽  
Representation Method ◽  
Speed Accuracy ◽  
Installment Options

AbstractThis article prices American-style continuous-installment options in the constant elasticity of variance (CEV) diffusion model where the volatility is a function of the stock price. We derive the semi-closed form formulas for the American continuous-installment options using Kim’s integral representation method and then obtain the closed-form solutions by approximating the optimal exercise and stopping boundaries as step functions. We demonstrate the speed-accuracy of our approach for different parameters of the CEV model. Furthermore, the effects on both option price and the optimal boundaries are discussed and the causes of underestimating or overestimating the option prices are analyzed under the classical Black-Scholes-Merton model, in particular, for the case of elasticity coefficient with numerical examples.

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