scholarly journals Optimal Asset Allocation for CRRA and CARA Insurers under the Vasicek Interest Rate Model

2022 ◽  
Vol 2022 ◽  
pp. 1-14
Author(s):  
Hanlei Hu ◽  
Shaoyong Lai ◽  
Hongjing Chen
Keyword(s):  
Interest Rate ◽  
Risk Aversion ◽  
Asset Allocation ◽  
Investment Strategy ◽  
Interest Rate Risk ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Rate Model ◽  
Rate Fluctuation ◽  
Interest Rate Model

This paper considers the reinsurance-investment problem with interest rate risks under constant relative risk aversion and constant absolute risk aversion preferences, respectively. Stochastic control theory and dynamic programming principle are applied to investigate the optimal proportional reinsurance-investment strategy for an insurer under the Vasicek stochastic interest rate model. Solving the corresponding Hamilton-Jacobi-Bellman equation via the Legendre transform approach, the optimal premium allocation strategies maximizing the expected utilities of terminal wealth are derived. In addition, several sensitivity analyses and numerical illustrations are given to analyze the impacts of different risk preferences and interest rate fluctuation on the optimal strategies. We find that the asset allocation and reinsurance ratio of the insurer are correlated with risk preference coefficient and interest rate fluctuation, and the insurance company may adjust the reinsurance-investment strategy to deal with interest rate risk.

scholarly journals Total Return Swap Valuation with Counterparty Risk and Interest Rate Risk

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Anjiao Wang ◽  
Zhongxing Ye
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Interest Rate Risk ◽  
Counterparty Risk ◽  
Rate Model ◽  
Change Of Measure ◽  
Market Interest Rate ◽  
Rate Risk ◽  
Interest Rate Model ◽  
The Interest Rate

We study the pricing of total return swap (TRS) under the contagion models with counterparty risk and the interest rate risk. We assume that interest rate follows Heath-Jarrow-Morton (HJM) forward interest rate model and obtain the Libor market interest rate. The cases where default is related to the interest rate and independent of interest rate are considered. Using the methods of change of measure and the “total hazard construction,” the joint default probabilities are obtained. Furthermore, we obtain the closed-form formulas of TRS under different contagion models, respectively.

scholarly journals Pricing of Embedded Options in Bank Deposits and Loans Based on Jump-Diffusion Interest Rate Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Enlin Tang ◽  
Song Xu
Keyword(s):  
Interest Rate ◽  
Commercial Banks ◽  
Jump Diffusion ◽  
Interest Rate Risk ◽  
Rate Model ◽  
Interest Rate Marketization ◽  
Interest Rate Model ◽  
Embedded Options ◽  
The Interest Rate ◽  
Interest Margin

The marketization of interest rate is an inevitable requirement for China’s financial reform and joining the WTO to connect with the international financial market. It is also an important link to improve the marketization degree of China’s financial system. The marketization of interest rate in China is gradually advancing according to its preset mode. In the process of interest rate marketization, an unavoidable problem is that while the interest rate marketization gives the commercial banks the autonomy of capital pricing, the fluctuation of interest rate is more and more frequent. However, due to the fluctuation of interest rate, the loan as the main assets of commercial banks will be prepayed by borrowers, and the time deposit as the main liabilities of commercial banks will be withdrawn by depositors in advance; that is, embedded options are implied in asset liability items, which makes it difficult for commercial banks to accurately calculate the actual interest margin of deposits and loans and manage the interest rate risk. Therefore, it is of great significance to identify and price such embedded option value. On the basis of identifying and decomposing the embedded options in deposit and loan of commercial banks, according to the change characteristics of deposit and loan interest rate of Chinese commercial banks, this paper chooses jump-diffusion interest rate model to describe the change of benchmark interest rate of deposit and loan in China and demonstrates the advantages of this model compared with other models. Based on Monte Carlo simulation technology, the embedded options of five-year fixed deposit and ten-year prepayable loan in China are priced. On this basis, it points out that the real interest margin of commercial bank’s deposit and loan should be the nominal interest margin minus the value of deposit and loan’s embedded options. In the process of interest rate risk management, we should pay attention to the existence of embedded options and carry out effective management.

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.

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