Upper bounds for ruin probabilities under stochastic interest rate and optimal investment strategies

2012 ◽  
Vol 28 (7) ◽  
pp. 1421-1430 ◽  
Author(s):  
Jin Zhu Li ◽  
Rong Wu
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Upper Bounds ◽  
Stochastic Interest Rate ◽  
Ruin Probabilities ◽  
Investment Strategies ◽  
Stochastic Interest

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 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 Optimal Investment Strategy under the CEV Model with Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yong He ◽  
Peimin Chen
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Stochastic Interest Rate ◽  
Model Parameters ◽  
Optimal Investment Strategy ◽  
Stochastic Interest ◽  
Cev Process ◽  
The Interest Rate

Interest rate is an important macrofactor that affects asset prices in the financial market. As the interest rate in the real market has the property of fluctuation, it might lead to a great bias in asset allocation if we only view the interest rate as a constant in portfolio management. In this paper, we mainly study an optimal investment strategy problem by employing a constant elasticity of variance (CEV) process and stochastic interest rate. The assets of investment for individuals are supposed to be composed of one risk-free asset and one risky asset. The interest rate for risk-free asset is assumed to follow the Cox–Ingersoll–Ross (CIR) process, and the price of risky asset follows the CEV process. The objective is to maximize the expected utility of terminal wealth. By applying the dual method, Legendre transformation, and asymptotic expansion approach, we successfully obtain an asymptotic solution for the optimal investment strategy under constant absolute risk aversion (CARA) utility function. In the end, some numerical examples are provided to support our theoretical results and to illustrate the effect of stochastic interest rates and some other model parameters on the optimal investment strategy.

scholarly journals Optimal Investment-Reinsurance Policy with Stochastic Interest and Inflation Rates

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xin Zhang ◽  
Xiaoxiao Zheng
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Optimal Decision ◽  
Stochastic Interest Rate ◽  
Security Market ◽  
Power Utility ◽  
Interest Rate Models ◽  
Classic Problem ◽  
Inflation Rates ◽  
Stochastic Interest

The aim of this paper is to study a classic problem in actuarial mathematics, namely, an optimal reinsurance-investment problem, in the presence of stochastic interest and inflation rates. This is of relevance since insurers make investment and risk management decisions over a relatively long horizon where uncertainty about interest rate and inflation rate may have significant impacts on these decisions. We consider the situation where three investment opportunities, namely, a savings account, a share, and a bond, are available to an insurer in a security market. In the meantime, the insurer transfers part of its insurance risk through acquiring a proportional reinsurance. The investment and reinsurance decisions are made so as to maximize an expected power utility on terminal wealth. An explicit solution to the problem is derived for each of the two well-known stochastic interest rate models, namely, the Ho–Lee model and the Vasicek model, using standard techniques in stochastic optimal control theory. Numerical examples are presented to illustrate the impacts of the two different stochastic interest rate modeling assumptions on optimal decision making of the insurer.

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