scholarly journals Optimal Consumption and Portfolio Decision with Convertible Bond in Affine Interest Rate and Heston’s SV Framework

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Hao Chang ◽  
Xue-Yan Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Separation Of Variables ◽  
Optimal Investment ◽  
Convertible Bond ◽  
Dynamic Programming Principle ◽  
Stochastic Dynamic ◽  
Special Cases ◽  
The Impact ◽  
Consumption Strategies

We are concerned with an optimal investment-consumption problem with stochastic affine interest rate and stochastic volatility, in which interest rate dynamics are described by the affine interest rate model including the Cox-Ingersoll-Ross model and the Vasicek model as special cases, while stock price is driven by Heston’s stochastic volatility (SV) model. Assume that the financial market consists of a risk-free asset, a zero-coupon bond (or a convertible bond), and a risky asset. By using stochastic dynamic programming principle and the technique of separation of variables, we get the HJB equation of the corresponding value function and the explicit expressions of the optimal investment-consumption strategies under power utility and logarithmic utility. Finally, we analyze the impact of market parameters on the optimal investment-consumption strategies by giving a numerical example.

scholarly journals Portfolio Selection with Liability and Affine Interest Rate in the HARA Utility Framework

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hao Chang ◽  
Kai Chang ◽  
Ji-mei Lu
Keyword(s):  
Interest Rate ◽  
Absolute Risk ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Management Problem ◽  
Power Utility ◽  
Special Cases ◽  
Hara Utility

This paper studied an asset and liability management problem with stochastic interest rate, where interest rate is assumed to be governed by an affine interest rate model, while liability process is driven by the drifted Brownian motion. The investors wish to look for an optimal investment strategy to maximize the expected utility of the terminal surplus under hyperbolic absolute risk aversion (HARA) utility function, which consists of power utility, exponential utility, and logarithm utility as special cases. By applying dynamic programming principle and Legendre transform, the explicit solutions for HARA utility are achieved successfully and some special cases are also discussed. Finally, a numerical example is provided to illustrate our results.

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.

scholarly journals Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2183
Author(s):  
Jiaqi Zhu ◽  
Shenghong Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Financial Market ◽  
Equilibrium Strategy ◽  
Stochastic Interest Rate ◽  
Programming Approach ◽  
Model Parameters ◽  
Stochastic Interest ◽  
The Impact ◽  
Mean Variance

This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process. The financial market consists of a risk-free asset, a bond, and a stock modelled by Heston’s stochastic volatility model. Interest rate in the market is modelled by the Vasicek model. By using extended dynamic programming approach, we explicitly derive equilibrium reinsurance-investment strategies and value functions. In addition, we provide and prove a verification theorem and then prove the solution we get satisfies it. Moreover, sensitive analysis is given to show the impact of several model parameters on equilibrium strategy and the efficient frontier.

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.

scholarly journals The Impact of Stock Prices on Consumption and Interest Rate in Turkey: Evidence from a Time Varying Vector Autoregressive Model

2014 ◽  
Author(s):  
Evrim Tören
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Open Economy ◽  
Stock Prices ◽  
Autoregressive Model ◽  
Time Varying ◽  
Vector Autoregressive Model ◽  
Macroeconomic Dynamics ◽  
Vector Autoregressive ◽  
The Impact

This paper aims to examine the spillovers from stock prices onto consumption and interest rate for Turkey by using a time-varying vector autoregressive model with stochastic volatility. A three-variable time-varying vector autoregressive model is estimated to capture the time-varying nature of the macroeconomic dynamics in the Turkish economy between real consumption, nominal interest rate and real stock prices. In order to obtain the macroeconomic dynamics in a small open economy, the data covers the period 1987:Q1 until 2013:Q3 in Turkey. The sample data is gathered from the official website of Central Bank of the Republic of Turkey. Overall, this study provides the evidence of significant time-varying spillovers on consumption and interest rate coming from the stock market during financial crises and implications of monetary policy in Turkey. In addition, a time-varying vector autoregressive model with stochastic volatility offers remarkable results about the impact of price shock on consumption levels in Turkey.

scholarly journals Robust optimal asset-liability management with penalization on ambiguity

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yu Yuan ◽  
Hui Mi
Keyword(s):  
Reference Model ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Programming Approach ◽  
Stochastic Dynamic ◽  
Economic Implication ◽  
Investment Strategies ◽  
Dynamic Programming Approach ◽  
Optimal Investment Strategy ◽  
Special Cases

<p style='text-indent:20px;'>In this paper, we study the robust optimal asset- problems for an ambiguity-averse investor, who does not have perfect information in the drift terms of the risky asset and liability processes. Two different kinds of objectives are considered: <inline-formula><tex-math id="M1">\begin{document}$ (i) $\end{document}</tex-math></inline-formula> Maximizing the minimal expected utility of the terminal wealth; <inline-formula><tex-math id="M2">\begin{document}$ (ii) $\end{document}</tex-math></inline-formula> Minimizing the maximal cumulative deviation. The ambiguity in both problems is described by a set of equivalent measures to the reference model. By the stochastic dynamic programming approach and Hamilton-Jacobi-Bellman (HJB) equation, we derive closed-form expressions for the value function and corresponding robust optimal investment strategy in each problem. Furthermore, some special cases are provided to investigate the effect of model uncertainty on the optimal investment strategy. Finally, the economic implication and parameter sensitivity are analyzed by some numerical examples. We also compare the robust optimal investment strategies in two different problems.</p>

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

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Optimal Investment ◽  
Stochastic Volatility Model ◽  
Power Utility ◽  
Variable Approach ◽  
Volatility Model ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman ◽  
Optimal Investment And Consumption

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.

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 Modeling the Effect of Interest Rate Uncertainty on Residents’ Consumption – Based on a DSGE Model Embedded Stochastic Volatility

2018 ◽  
Vol 22 (6) ◽  
pp. 846-852
Author(s):  
Xiaowen Hu ◽  
◽  
Chengchen Hu ◽  
Yiyu Yao
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Negative Impact ◽  
Structural Equations ◽  
Stochastic Volatility Model ◽  
Current Period ◽  
Volatility Model ◽  
Dynamic Stochastic ◽  
The Government ◽  
The Impact

Modeling the effect of uncertainty shock usually employs VAR method. The approach however often leads to the results unstable with different structural equations. Especially it is modeled without a microscopic basis which often implies wrong policy advice. A new method to model the effect of interest rate uncertainty is proposed in this paper that overcomes this limitation. A stochastic volatility model is embedded into a dynamic stochastic general equilibrium framework to study the influence of interest rate uncertainty on the residents’ consumption. Using the third-order perturbation method to identify the impact of interest rate uncertainty on consumption. It is found by simulation that with the interest rate uncertainty increased, the consumption of residents in the current period has obviously decreased due to the preventive saving mechanism. Variance analysis shows that interest rate uncertainty shocks can explain 8% share of consumption volatility. The empirical results are robust when changing the parameter values and the prior distribution of the parameters. The conclusion shows the government should strengthen to guide the public reasonable expectations, to avoid the negative impact of interest rate uncertainty.

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