scholarly journals An Optimal Portfolio Problem of DC Pension with Input-Delay and Jump-Diffusion Process

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Weixiang Xu ◽  
Jinggui Gao
Keyword(s):  
Diffusion Process ◽  
Control Problem ◽  
Jump Diffusion ◽  
Investment Strategy ◽  
Optimal Portfolio ◽  
Input Delay ◽  
Programming Approach ◽  
Time Interval ◽  
Stochastic Dynamic ◽  
Jump Diffusion Process

In this paper, an optimal portfolio control problem of DC pension is studied where the time interval between the implementation of investment behavior and its effectiveness (hereafter input-delay) is particularly focused. There are two assets available for investment: a risk-free cash bond and a risky stock with a jump-diffusion process. And the wealth process of the pension fund is modeled as a stochastic delay differential equation. To secure a comfortable retirement life for pension members and also avoid excessive risk, the fund managers in this paper aim to minimize the expected value of quadratic deviations between the actual terminal fund scale and a preset terminal target. By applying the stochastic dynamic programming approach and the match method, the optimal portfolio control problem is solved and the closed-form solution is obtained. In addition, an algorithm is developed to calculate the numerical solution of the optimal strategy. Finally, we have performed a sensitivity analysis to explore how the managers’ preset terminal target, the length of input-delay, and the jump intensity of risky assets affect the optimal investment strategy.

scholarly journals Optimal Reinsurance-Investment Problem for an Insurer and a Reinsurer with Jump-Diffusion Process

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Hanlei Hu ◽  
Zheng Yin ◽  
Xiujuan Gao
Keyword(s):  
Diffusion Process ◽  
Optimal Strategies ◽  
Jump Diffusion ◽  
Sensitivity Analyses ◽  
Programming Approach ◽  
Investment Strategies ◽  
Optimal Reinsurance ◽  
Bellman Equations ◽  
Dynamic Programming Approach ◽  
Jump Diffusion Process

The optimal reinsurance-investment strategies considering the interests of both the insurer and reinsurer are investigated. The surplus process is assumed to follow a jump-diffusion process and the insurer is permitted to purchase proportional reinsurance from the reinsurer. Applying dynamic programming approach and dual theory, the corresponding Hamilton-Jacobi-Bellman equations are derived and the optimal strategies for exponential utility function are obtained. In addition, several sensitivity analyses and numerical illustrations in the case with exponential claiming distributions are presented to analyze the effects of parameters about the optimal strategies.

OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS

2021 ◽  
pp. 1-25
Author(s):  
CAIBIN ZHANG ◽  
ZHIBIN LIANG ◽  
KAM CHUEN YUEN
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Optimal Portfolio ◽  
Dynamic Programming Principle ◽  
Pure Diffusion ◽  
Special Cases ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

Abstract We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.

Optimal portfolio and consumption for a Markovian regime-switching jump-diffusion process

2021 ◽  
Vol 63 ◽  
pp. 308-332
Author(s):  
Caibin Zhang ◽  
Zhibin Liang ◽  
Kam Chuen Yuen
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Optimal Portfolio ◽  
Dynamic Programming Principle ◽  
Pure Diffusion ◽  
Special Cases ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.   doi:10.1017/S1446181121000122

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