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 Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shuang Li ◽  
Shican Liu ◽  
Yanli Zhou ◽  
Yonghong Wu ◽  
Xiangyu Ge
Keyword(s):  
Optimal Control ◽  
Interest Rate ◽  
Differential Equations ◽  
Risk Aversion ◽  
Hjb Equation ◽  
Time Inconsistency ◽  
Equilibrium Strategy ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Mean Variance

In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the optimal control over the financial system involving stochastic interest rate and state-dependent risk aversion (SDRA) mean-variance utility. By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. Finally, the numerical examples provided are used to analyze how stochastic (short-term) interest rates and risk aversion affect the optimal control strategies to illustrate the validity of our results.

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.

Effect of Prepayment and Call Limit on the Duration of CMO (Multi-tranche MBS): Full vs. Partial Pass-Through Structure

2012 ◽  
Vol 20 (4) ◽  
pp. 391-425
Author(s):  
Yun Woo Park ◽  
Doo Won Bang
Keyword(s):  
Interest Rate ◽  
Empirical Research ◽  
Stochastic Interest Rate ◽  
Mortgage Loans ◽  
Prepayment Risk ◽  
Residential Mortgage ◽  
Stochastic Interest ◽  
Pass Through ◽  
The Impact

Residential mortgage loans as well as the MBS (mortgage-backed security), which securitizes these loans, are exposed to prepayment risk. We examine the effect of prepayment process on the duration of the CMO (multi-tranche MBS). In particular, we examine the effect of partial pass-through where there is a call limit expressed as a percentage of initial tranche balance. Due to the absence of empirical research on the CMO duration, neither the actual CMO duration nor the determinants of the CMO duration have been reported. Our study reports the actual CMO duration and the determinants of the CMO duration. By showing that the CMO duration is much shorter than the nominal time-to-maturity we point to the need to search for longer duration MBS structures. We find that in both the deterministic and stochastic interest rate environments duration is reduced as prepayment speed rises and duration rises as call limit decreases. We make contribution to the literature by shedding light on the effect of prepayment and call limit on the duration of multi-tranche MBS. In particular, this research characterizes the impact of the partial pass-through structuring approach on the CMO duration as well as CMO pricing. Finally, it assists CMO investors in better assessing and managing reinvestment risks of pass-through products.

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