A Game Theoretic Algorithm to Solve Riccati and Hamilton—Jacobi—Bellman—Isaacs (HJBI) Equations in H ∞ Control

This paper investigates some differential game applications to option pricing mechanisms and related problems. Two players, an investor and "Nature", play a zero-sum game. The usual uncertainty modelling (log-normality for instance) in systems describing the price evolution of stocks is replaced by "Nature", a player who counteracts the investor as much as possible. A relationship between a restricted version of the Black-Scholes and the Hamilton-Jacobi-Bellman partial differential equations is given. This paper, is a first step to possibly solve various option pricing problems (with constraints and/or transactions costs for instance) by means of the available numerical software for optimal control problems. In the second part of the paper, another model, now with three players, is considered. The third player is the bank interested in maximising its own profits by choosing the right formula for transaction costs. Thus a three-person nonzero-sum game, with a special kind of Stackelberg information structure, results. Some simple examples hint in the direction that the bank will be a clear winner.

Download Full-text

Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles

RAIRO - Operations Research ◽

10.1051/ro/2021183 ◽

2021 ◽

Author(s):

Junna Bi ◽

Danping Li ◽

Nan Zhang

Keyword(s):

Investment Strategy ◽

Expected Value ◽

Value Premium ◽

Equilibrium Strategy ◽

Model Parameters ◽

Optimal Reinsurance ◽

Investment Problem ◽

Common Shock ◽

Game Theoretic ◽

Hamilton Jacobi Bellman

This paper investigates the optimal mean-variance reinsurance-investment problem for an insurer with a common shock dependence under two kinds of popular premium principles: the variance premium principle and the expected value premium principle. We formulate the optimization problem within a game theoretic framework and derive the closed-form expressions of the equilibrium reinsurance-investment strategy and equilibrium value function under the two different premium principles by solving the extended Hamilton-Jacobi-Bellman system of equations. We find that under the variance premium principle, the proportional reinsurance is the optimal reinsurance strategy for the optimal reinsurance-investment problem with a common shock, while under the expected value premium principle, the excess-of-loss reinsurance is the optimal reinsurance strategy. In addition, we illustrate the equilibrium reinsurance-investment strategy by numerical examples and discuss the impacts of model parameters on the equilibrium strategy.

Download Full-text

Game-Theoretic Analysis of Interaction between Dynamic Variable Pricing and Dynamic Traffic Assignment

Applications of Advanced Technologies in Transportation Engineering (2004) ◽

10.1061/40730(144)108 ◽

2004 ◽

Cited By ~ 1

Author(s):

Xizhao Zhou ◽

Bayi Zhou ◽

Yan Li

Keyword(s):

Traffic Assignment ◽

Dynamic Traffic Assignment ◽

Theoretic Analysis ◽

Dynamic Traffic ◽

Dynamic Variable ◽

Game Theoretic Analysis ◽

Variable Pricing ◽

Game Theoretic

Download Full-text

Stability in the informal value transfer systems: norms of trust or institutions of control?

Voprosy Ekonomiki ◽

10.32609/0042-8736-2017-3-120-130 ◽

2017 ◽

pp. 120-130

Author(s):

A. Lyasko

Keyword(s):

Social Control ◽

Institutional Economics ◽

Theoretic Model ◽

Transfer System ◽

Value Transfer ◽

Partner Interaction ◽

Game Theoretic ◽

Game Theoretic Model ◽

Informal Value Transfer System

Informal financial operations exist in the shadow of official regulation and cannot be protected by the formal legal instruments, therefore raising concerns about the enforcement of obligations taken by their participants. This paper analyzes two alternative types of auxiliary institutions, which can coordinate expectations of the members of informal value transfer systems, namely attitudes of trust and norms of social control. It offers some preliminary approaches to creating a game-theoretic model of partner interaction in the informal value transfer system. It also sheds light on the perspectives of further studies in this area of institutional economics.

Download Full-text

Influential individuals: Approach to modeling

Voprosy Ekonomiki ◽

10.32609/0042-8736-2018-9-114-131 ◽

2018 ◽

pp. 114-131

Author(s):

O. Yu. Bondarenko

Keyword(s):

Social Interactions ◽

Social Status ◽

Experimental Approach ◽

Expert Knowledge ◽

Formal Models ◽

Leader Influence ◽

Learning Game ◽

Game Theoretic ◽

Asymmetric Interactions ◽

Influential Individuals

his article explores theoretical and experimental approach to modeling social interactions. Communication and exchange of information with other people affect individual’s behavior in numerous areas. Generally, such influence is exerted by leaders, outstanding individuals who have a higher social status or expert knowledge. Social interactions are analyzed in the models of social learning, game theoretic models, conformity models, etc. However, there is a lack of formal models of asymmetric interactions. Such models could help elicit certain qualities characterizing higher social status and perception of status by other individuals, find the presence of leader influence and analyze its mechanism.

Download Full-text