Open-Loop Equilibrium Strategy for Mean-Variance Portfolio Problem Under Stochastic Volatility

2018 ◽  
Author(s):  
Tingjin Yan ◽  
Hoi Ying Wong
Keyword(s):  
Stochastic Volatility ◽  
Open Loop ◽  
Equilibrium Strategy ◽  
Portfolio Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance

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.

scholarly journals Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Liming Zhang ◽  
Rongming Wang ◽  
Jiaqin Wei
Keyword(s):  
Convex Set ◽  
Investment Strategy ◽  
Open Loop ◽  
Equilibrium Strategy ◽  
Investment Strategies ◽  
Risky Investment ◽  
New Business ◽  
New Policies ◽  
Risk Processes ◽  
Mean Variance

<p style='text-indent:20px;'>In this paper, we study a general mean-variance reinsurance, new business and investment problem, where the claim processes of original and new businesses are modeled by two different risk processes and the safety loadings of reinsurance and new business are different. The retention level of the insurer is constrained in <inline-formula><tex-math id="M1">\begin{document}$ [0,1] $\end{document}</tex-math></inline-formula> and the controls of new business and risky investment are required to be non-negative. This model relaxes the limitations of those in existing research. By using the projection onto the convex set controls valued in, we obtain an open-loop equilibrium reinsurance-new business-investment strategy explicitly. We also show that the obtained equilibrium strategy is the optimal one among all deterministic strategies in the sense that it yields the smallest mean-variance cost. In the case where original and new businesses are the same, the equilibrium strategy is given in closed-form and its sensitivities to safety loadings are shown by numerical examples. At last, by comparing with the case where acquiring new business is prohibited, we show that allowing writing new policies indeed improves the performance of the insurer's risk management.</p>

scholarly journals Time-Consistent Strategies for a Multiperiod Mean-Variance Portfolio Selection Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Huiling Wu
Keyword(s):  
Nash Equilibrium ◽  
Portfolio Selection ◽  
Optimization Problems ◽  
Selection Problem ◽  
Equilibrium Strategy ◽  
Nash Equilibrium Strategy ◽  
Portfolio Selection Problem ◽  
Nash Equilibrium Strategies ◽  
Mean Variance Portfolio ◽  
Mean Variance

It remained prevalent in the past years to obtain the precommitment strategies for Markowitz's mean-variance portfolio optimization problems, but not much is known about their time-consistent strategies. This paper takes a step to investigate the time-consistent Nash equilibrium strategies for a multiperiod mean-variance portfolio selection problem. Under the assumption that the risk aversion is, respectively, a constant and a function of current wealth level, we obtain the explicit expressions for the time-consistent Nash equilibrium strategy and the equilibrium value function. Many interesting properties of the time-consistent results are identified through numerical sensitivity analysis and by comparing them with the classical pre-commitment solutions.

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