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.

Stochastic interest rate models

2018 ◽  
pp. 195-208
Author(s):  
Erik Lindström ◽  
Henrik Madsen ◽  
Jan Nygaard Nielsen
Keyword(s):  
Interest Rate ◽  
Stochastic Interest Rate ◽  
Interest Rate Models ◽  
Stochastic Interest

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.

Value-at-Risk estimation with stochastic interest rate models for option-bond portfolios

2017 ◽  
Vol 21 ◽  
pp. 10-20 ◽  
Author(s):  
Xiaoyu Wang ◽  
Dejun Xie ◽  
Jingjing Jiang ◽  
Xiaoxia Wu ◽  
Jia He
Keyword(s):  
At Risk ◽  
Interest Rate ◽  
Value At Risk ◽  
Risk Estimation ◽  
Stochastic Interest Rate ◽  
Interest Rate Models ◽  
Stochastic Interest ◽  
Bond Portfolios

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.

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