3 Risk Aversion with State-Dependent Preferences: Some Economic Applications

1985 ◽  
pp. 45-60
Keyword(s):  
Risk Aversion ◽  
Economic Applications ◽  
State Dependent

scholarly journals Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 108 ◽  
Author(s):  
Liyuan Wang ◽  
Zhiping Chen
Keyword(s):  
Risk Aversion ◽  
Stochastic Game ◽  
Pension Plan ◽  
Time Inconsistency ◽  
State Variables ◽  
Economic Point ◽  
State Dependent ◽  
Equilibrium Control ◽  
Special Cases ◽  
Game Theoretic

When facing a multi-period defined contribution (DC) pension plan investment problem during the accumulation phase, the risk aversion attitude of a mean-variance investor may depend on state variables. In this paper, we propose a state-dependent risk aversion model which is a linear function of the current wealth level after contribution. This risk aversion model is reasonable from both the dimensional analysis and the economic point of view. Moreover, we incorporate the wage income factor into our model. In the field of dynamic investment analysis, most studies have irrational situations in their models because of the lack of the positiveness for the wealth process. In view of it, we further improve the work of Wang and Chen by completely eliminating the irrationality of the model. Due to the time-inconsistency of the resulting stochastic control problem, we derive the explicit expressions of the equilibrium control and the corresponding equilibrium value function by adopting the game theoretic framework developed in Björk and Murgoci. Further, two special cases are discussed. Finally, using a more realistic risk aversion coefficient, we provide a series of empirical tests based on the real data from the American market and compare our results with the relevant results in the literature.

scholarly journals Option pricing with random risk aversion

2022 ◽  
Author(s):  
Luiz Vitiello ◽  
Ser-Huang Poon
Keyword(s):  
Risk Aversion ◽  
Implied Volatility ◽  
Market Volatility ◽  
European Options ◽  
Parameter Change ◽  
Pricing Kernel ◽  
Underlying Asset ◽  
State Dependent ◽  
Low Levels ◽  
Aggregate Wealth

AbstractBased on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent, and aggregate wealth and the underlying asset have a bivariate transformed-normal distribution. Our results show that the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel, and that, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Also, we demonstrate that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. An empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

scholarly journals Nash Equilibrium Strategy for a DC Pension Plan with State-Dependent Risk Aversion: A Multiperiod Mean-Variance Framework

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Liyuan Wang ◽  
Zhiping Chen
Keyword(s):  
Risk Aversion ◽  
Pension Plan ◽  
Time Inconsistency ◽  
Equilibrium Strategy ◽  
Defined Contribution ◽  
Nash Equilibrium Strategy ◽  
State Dependent ◽  
Special Cases ◽  
Fractional Function ◽  
Mean Variance

This paper investigates a defined contribution (DC) pension plan investment problem during the accumulation phase under the multiperiod mean-variance criterion. Different from most studies in the literature, where the investor’s risk aversion attitude is state-independent, we choose a state-dependent risk aversion parameter, which is a fractional function of the current wealth level. Moreover, we incorporate the wage income factor into our model, which leads to a more complicated problem than the portfolio selection problems that appeared in relevant papers. Due to the time inconsistency of the resulting problem, we derive the explicit expressions for the equilibrium strategy and the corresponding equilibrium value function by adopting the game theoretic framework and using the extended Bellman equation. Further, two special cases are discussed. Finally, based on real data from the American market, some prominent features of the equilibrium strategy established in our theoretical derivations are provided by comparing them with the results in the existing literature.

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