Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utility

2009 ◽  
Vol 25 (3) ◽  
pp. 407-420 ◽  
Author(s):  
Jinzhu Li ◽  
Rong Wu
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Optimal Investment ◽  
Stochastic Interest Rate ◽  
Power Utility ◽  
Investment Problem ◽  
Stochastic Interest ◽  
Optimal Investment Problem

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 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-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.

PRICING VARIANCE SWAPS UNDER DOUBLE HESTON STOCHASTIC VOLATILITY MODEL WITH STOCHASTIC INTEREST RATE

2021 ◽  
pp. 1-17
Author(s):  
Huojun Wu ◽  
Zhaoli Jia ◽  
Shuquan Yang ◽  
Ce Liu
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Stochastic Interest Rate ◽  
Modeling Framework ◽  
Variance Swaps ◽  
Volatility Model ◽  
Stochastic Interest

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

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.

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