scholarly journals Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chubing Zhang ◽  
Ximing Rong
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Legendre Transform ◽  
Investment Strategies ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Plan Member ◽  
Cara Utility ◽  
Hamilton Jacobi Bellman ◽  
Coupon Bond

We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

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 TheCEVModel and Its Application in a Study of Optimal Investment Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Aiyin Wang ◽  
Ls Yong ◽  
Yang Wang ◽  
Xuanjun Luo
Keyword(s):  
Optimal Investment ◽  
Investment Strategy ◽  
Legendre Transform ◽  
Investment Strategies ◽  
Approximation Solution ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Optimal Investment Strategy ◽  
Hamilton Jacobi Bellman ◽  
Exponential Utility Function

The constant elasticity of variance (CEV) model is used to describe the price of the risky asset. Maximizing the expected utility relating to the Hamilton-Jacobi-Bellman (HJB) equation which describes the optimal investment strategies, we obtain a partial differential equation. Applying the Legendre transform, we transform the equation into a dual problem and obtain an approximation solution and an optimal investment strategies for the exponential utility function.

scholarly journals The Optimal Strategy of Reinsurance-Investment Problem for an Insurer with Dynamic Income Under Stochastic Interest Rate

2016 ◽  
Vol 4 (3) ◽  
pp. 244-257
Author(s):  
Delei Sheng
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Control Technique ◽  
Stochastic Interest Rate ◽  
Insurance Company ◽  
Power Utility ◽  
Investment Problem ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman ◽  
Constant Interest Rate

AbstractThis paper considers the reinsurance-investment problem for an insurer with dynamic income to balance the profit of insurance company and policy-holders. The insurer’s dynamic income is given by a net premium minus a dynamic reward budget item and the net premium is obtained according to the expected premium principle. Applying the stochastic control technique, a Hamilton-Jacobi-Bellman equation is established under stochastic interest rate model and the explicit solution is obtained by maximizing the insurer’s power utility of terminal wealth. In addition, the comparison with corresponding results under constant interest rate helps us to understand the role and influence of stochastic interest rates more in-depth.

scholarly journals Explicit Solution of Reinsurance-Investment Problem for an Insurer with Dynamic Income under Vasicek Model

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
De-Lei Sheng
Keyword(s):  
Explicit Solution ◽  
Bellman Equation ◽  
Control Technique ◽  
Power Utility ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Interest Rate Model ◽  
Hamilton Jacobi Bellman

Unlike traditionally used reserves models, this paper focuses on a reserve process with dynamic income to study the reinsurance-investment problem for an insurer under Vasicek stochastic interest rate model. The insurer’s dynamic income is given by the remainder after a dynamic reward budget being subtracted from the insurer’s net premium which is calculated according to expected premium principle. Applying stochastic control technique, a Hamilton-Jacobi-Bellman equation is established and the explicit solution is obtained under the objective of maximizing the insurer’s power utility of terminal wealth. Some economic interpretations of the obtained results are explained in detail. In addition, numerical analysis and several graphics are given to illustrate our results more meticulous.

scholarly journals OPTIMAL HEDGING OF DERIVATIVES WITH TRANSACTION COSTS

2006 ◽  
Vol 09 (07) ◽  
pp. 1051-1069 ◽  
Author(s):  
ERIK AURELL ◽  
PAOLO MURATORE-GINANNESCHI
Keyword(s):  
Transaction Costs ◽  
Optimization Problem ◽  
Optimal Investment ◽  
Market Model ◽  
Black Scholes ◽  
Hamilton Jacobi Bellman Equation ◽  
Finite Time Horizon ◽  
Hamilton Jacobi Bellman ◽  
Delta Hedge ◽  
Strong Control

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton–Jacobi–Bellman equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at hand, these conditions simply imply arbitrage-free ("Black–Scholes") pricing of the derivative. While pricing is hence not changed by friction allow a portfolio to fluctuate around a delta hedge. In the limit of weak friction, we determine the optimal control to essentially be of two parts: a strong control, which tries to bring the stock-and-derivative portfolio towards a Black–Scholes delta hedge; and a weak control, which moves the portfolio by adding or subtracting a Black–Scholes hedge. For simplicity we assume growth-optimal investment criteria and quadratic friction.

scholarly journals Optimal Investment for Insurers with the Extended CIR Interest Rate Model

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Mei Choi Chiu ◽  
Hoi Ying Wong
Keyword(s):  
Interest Rate ◽  
Closed Form Solution ◽  
Critical Factor ◽  
Compound Poisson Process ◽  
Optimal Investment ◽  
Form Solution ◽  
Insurance Companies ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Jump Diffusion Model

A fundamental challenge for insurance companies (insurers) is to strike the best balance between optimal investment and risk management of paying insurance liabilities, especially in a low interest rate environment. The stochastic interest rate becomes a critical factor in this asset-liability management (ALM) problem. This paper derives the closed-form solution to the optimal investment problem for an insurer subject to the insurance liability of compound Poisson process and the stochastic interest rate following the extended CIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochastic interest rate when she invests in stocks and bonds. Our problem involves maximizing the expected constant relative risk averse (CRRA) utility function subject to stochastic interest rate and Poisson shocks. After solving the stochastic optimal control problem with the HJB framework, we offer a verification theorem by proving the uniform integrability of a tight upper bound for the objective function.

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 Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion

2021 ◽  
Author(s):  
Bohan Li ◽  
Junyi Guo
Keyword(s):  
Optimal Strategy ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Capital Asset Pricing ◽  
Investment Strategies ◽  
Asset Pricing Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Zero Sum ◽  
Mean Variance

This paper considers the optimal investment-reinsurance problem under the monotone mean-variance preference. The monotone mean-variance preference is a monotone version of the classical mean-variance preference. First of all, we reformulate the original problem as a zero-sum stochastic differential game. Secondly, the optimal strategy and the optimal value function for the monotone mean-variance problem are derived by the approach of dynamic programming and the Hamilton-Jacobi-Bellman-Isaacs equation. Thirdly, the efficient frontier is obtained and it is proved that the optimal strategy is an efficient strategy. Finally, the continuous-time monotone capital asset pricing model is derived.

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