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 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.

Optimal dynamic reinsurance with common shock dependence and state-dependent risk aversion

2019 ◽  
Vol 06 (01) ◽  
pp. 1950004
Author(s):  
Caibin Zhang ◽  
Zhibin Liang ◽  
Kam Chuen Yuen
Keyword(s):  
Risk Aversion ◽  
Risk Model ◽  
Optimal Strategies ◽  
Model Parameters ◽  
Compound Poisson ◽  
State Dependent ◽  
Optimal Dynamic ◽  
Game Theoretic ◽  
Time Inconsistent ◽  
The Impact

This paper studies an optimal dynamic proportional reinsurance in a risk model with two dependent classes of insurance business. Under the criterion of maximizing the mean–variance utility of the terminal wealth with state-dependent risk aversion, we formulate the time-inconsistent problem within a game theoretic framework. By the technique of stochastic control theory, explicit expressions of the optimal results are derived not only for diffusion risk model but also for compound Poisson risk model. Furthermore, the similar problem with constant risk aversion is studied as well. Finally, some numerical examples are presented to show the impact of model parameters on the optimal strategies for both compound Poisson and diffusion cases.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishak Alia ◽  
Farid Chighoub
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Optimal Time ◽  
Uniqueness Results ◽  
State Dependent ◽  
Consistent Solution ◽  
Game Theoretic ◽  
Markov Modulated ◽  
Mean Variance Portfolio ◽  
Mean Variance

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

Mean-variance equilibrium asset-liability management strategy with cointegrated assets

2021 ◽  
Vol 62 ◽  
pp. 209-234
Author(s):  
Mei Choi Chiu
Keyword(s):  
Financial Market ◽  
Time Consistency ◽  
Time Inconsistency ◽  
Asset Liability Management ◽  
Risky Assets ◽  
Liability Management ◽  
Equilibrium Control ◽  
Management Problems ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

This paper investigates asset-liability management problems in a continuous-time economy. When the financial market consists of cointegrated risky assets, institutional investors attempt to make profit from the cointegration feature on the one hand, while on the other hand they need to maintain a stable surplus level, that is, the company’s wealth less its liability. Challenges occur when the liability is random and cannot be fully financed or hedged through the financial market. For mean–variance investors, an additional concern is the rational time-consistency issue, which ensures that a decision made in the future will not be restricted by the current surplus level. By putting all these factors together, this paper derives a closed-form feedback equilibrium control for time-consistent mean–variance asset-liability management problems with cointegrated risky assets. The solution is built upon the Hamilton–Jacobi–Bellman framework addressing time inconsistency. doi: 10.1017/S1446181120000164

A Novel Approach for Analyzing Single Buffer Queueing Systems with State-Dependent Vacation and Correlated Input Process under Four Different Service Disciplines

2015 ◽  
Vol 6 (3) ◽  
pp. 19-59 ◽  
Author(s):  
Thomas Yew Sing Lee
Keyword(s):  
Performance Measures ◽  
Probability Generating Function ◽  
Performance Measure ◽  
Idle Time ◽  
Separate Analysis ◽  
Input Process ◽  
State Dependent ◽  
Special Cases ◽  
Service Disciplines ◽  
Different Types

The author presents performance analysis of a single buffer multiple-queue system. Four different types of service disciplines (i.e., non-preemptive, pre-emptive repeat different, state dependent random polling and globally gated) are analyzed. His model includes correlated input process and three different types of non-productive time (i.e., switchover, vacation and idle time). Special cases of the model includes server with mixed multiple and single vacations, stopping server with delayed vacation and stopping server with alternating vacation and idle time. For each of the four service disciplines the key performance measures such as average customer waiting time, loss probability, and throughput are computed. The results permit a detailed discussion of how these performance measures depends on the customer arrival rate, the customer service time, the switchover time, the vacation time, and the idle time. Moreover, extensive numerical results are presented and the four service disciplines are compared with respect to the performance measure. Previous studies of the single buffer multiple-queue systems tend to provide separate analysis for the two cases of zero and nonzero switchover time. The author is able to provide a unified analysis for the two cases. His results generalize and improve a number of known results on single buffer multiple-queue systems. Furthermore, this method does not require differentiation while it is needed if one uses the probability generating function approach. Lastly, the author's approach works for all single buffer multiple-queue systems in which the next queue to be served is determines solely on the basis of the occupancy states at the end of the cycle time.

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