scholarly journals ON A NEW PARADIGM OF OPTIMAL REINSURANCE: A STOCHASTIC STACKELBERG DIFFERENTIAL GAME BETWEEN AN INSURER AND A REINSURER

2018 ◽  
Vol 48 (02) ◽  
pp. 905-960 ◽  
Author(s):  
Lv Chen ◽  
Yang Shen
Keyword(s):  
Differential Game ◽  
Continuous Time ◽  
Stackelberg Game ◽  
General Setting ◽  
Random Coefficients ◽  
Stackelberg Equilibrium ◽  
New Paradigm ◽  
Optimal Reinsurance ◽  
Stackelberg Differential Game ◽  
Special Case

AbstractThis paper proposes a new continuous-time framework to analyze optimal reinsurance, in which an insurer and a reinsurer are two players of a stochastic Stackelberg differential game, i.e., a stochastic leader-follower differential game. This allows us to determine optimal reinsurance from joint interests of the insurer and the reinsurer, which is rarely considered in the continuous-time setting. In the Stackelberg game, the reinsurer moves first and the insurer does subsequently to achieve a Stackelberg equilibrium toward optimal reinsurance arrangement. Speaking more precisely, the reinsurer is the leader of the game and decides on an optimal reinsurance premium to charge, while the insurer is the follower of the game and chooses an optimal proportional reinsurance to purchase. Under utility maximization criteria, we study the game problem starting from the general setting with generic utilities and random coefficients to the special case with exponential utilities and constant coefficients. In the special case, we find that the reinsurer applies the variance premium principle to calculate the optimal reinsurance premium and the insurer's optimal ceding/retained proportion of insurance risk depends not only on the risk aversion of itself but also on that of the reinsurer.

scholarly journals Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Kai Du ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mean Field ◽  
Open Loop ◽  
Stackelberg Equilibrium ◽  
Linear Quadratic ◽  
Stackelberg Differential Game ◽  
Lq Optimal Control

This paper is concerned with a new kind of Stackelberg differential game of mean-field backward stochastic differential equations (MF-BSDEs). By means of four Riccati equations (REs), the follower first solves a backward mean-field stochastic LQ optimal control problem and gets the corresponding open-loop optimal control with the feedback representation. Then the leader turns to solve an optimization problem for a 1×2 mean-field forward-backward stochastic differential system. In virtue of some high-dimensional and complicated REs, we obtain the open-loop Stackelberg equilibrium, and it admits a state feedback representation. Finally, as applications, a class of stochastic pension fund optimization problems which can be viewed as a special case of our formulation is studied and the open-loop Stackelberg strategy is obtained.

A STACKELBERG GAME OF INNOVATION DIFFUSION: PRICING, ADVERTISING AND SUBSIDY STRATEGIES

2001 ◽  
Vol 03 (04) ◽  
pp. 325-339 ◽  
Author(s):  
LUIGI DE CESARE ◽  
ANDREA DI LIDDO
Keyword(s):  
Innovation Diffusion ◽  
Differential Game ◽  
Stackelberg Game ◽  
New Product ◽  
Public Authority ◽  
Optimal Price ◽  
Advertising Strategy ◽  
Stackelberg Differential Game ◽  
Set Up

We consider a firm that wishes to maximise the profits coming from the sale of a new product or technology by determining an optimal price and advertising strategy. A public authority wishes to accelerate and stimulate the adoption of the new product by using a budget to give price subsidies directly to the consumers. The problem is set up as a Stackelberg differential game.

Effect of the Return Policy in a Continuous-Time Newsvendor Problem

2017 ◽  
Vol 34 (06) ◽  
pp. 1750031
Author(s):  
Weiwei Zhang ◽  
Zhongfei Li ◽  
Ke Fu ◽  
Fan Wang
Keyword(s):  
Diffusion Process ◽  
Continuous Time ◽  
Existence And Uniqueness ◽  
Stackelberg Game ◽  
Jump Diffusion ◽  
Newsvendor Problem ◽  
Stackelberg Equilibrium ◽  
Computational Results ◽  
Return Policy ◽  
Demand Rate

This paper studies the stochastic differential Stackelberg game in a continuous-time newsvendor problem with a return policy, in which one supplier sells products to one retailer and the two parties make the decisions sequentially to maximize their own expected profits. When the demand process is a general jump-diffusion process, we provide a general formula for the equilibrium if it exists. When the demand rate is an Ornstein–Uhlenbeck (O–U) process, we prove the existence and uniqueness of the equilibrium and find an explicit expression for the equilibrium. Computational results show that the return policy has significant impact on the Stackelberg equilibrium.

scholarly journals Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

2020 ◽  
Vol 26 ◽  
pp. 83
Author(s):  
Jingtao Shi ◽  
Guangchen Wang ◽  
Jie Xiong
Keyword(s):  
Differential Game ◽  
Direct Calculation ◽  
Stackelberg Equilibrium ◽  
Equilibrium Strategy ◽  
Optimal Controls ◽  
State Variables ◽  
Linear Quadratic ◽  
Stochastic Filtering ◽  
Stackelberg Differential Game ◽  
The Cost

This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term “overlapping” means that there are common part between the follower’s and the leader’s information, while they have no inclusion relation. Optimal controls of the follower and the leader are obtained by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to give the state estimate feedback representation of the Stackelberg equilibrium strategy, while its solvability is a rather difficult open problem. A special case is then studied and is applied to the continuous-time principal-agent problem.

scholarly journals Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

2021 ◽  
Author(s):  
Yves Achdou ◽  
Jiequn Han ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions ◽  
Benjamin Moll
Keyword(s):  
Continuous Time ◽  
Wealth Distribution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heterogeneous Agent ◽  
Saving Behavior ◽  
Income And Wealth Distribution ◽  
Heterogeneous Agent Models ◽  
Special Case

Abstract We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

scholarly journals Optimal Decision-Making to Charge Electric Vehicles in Heterogeneous Networks: Stackelberg Game Approach

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 325 ◽  
Author(s):  
Shijun Chen ◽  
Huwei Chen ◽  
Shanhe Jiang
Keyword(s):  
Electric Vehicles ◽  
Heterogeneous Networks ◽  
Demand Uncertainty ◽  
Stackelberg Game ◽  
Optimal Solution ◽  
Stackelberg Equilibrium ◽  
Optimal Decision ◽  
Charging Station ◽  
Simulation Results ◽  
Grid Operators

Electric vehicles (EVs) are designed to improve the efficiency of energy and prevent the environment from being polluted, when they are widely and reasonably used in the transport system. However, due to the feature of EV’s batteries, the charging problem plays an important role in the application of EVs. Fortunately, with the help of advanced technologies, charging stations powered by smart grid operators (SGOs) can easily and conveniently solve the problems and supply charging service to EV users. In this paper, we consider that EVs will be charged by charging station operators (CSOs) in heterogeneous networks (Hetnet), through which they can exchange the information with each other. Considering the trading relationship among EV users, CSOs, and SGOs, we design their own utility functions in Hetnet, where the demand uncertainty is taken into account. In order to maximize the profits, we formulate this charging problem as a four-stage Stackelberg game, through which the optimal strategy is studied and analyzed. In the Stackelberg game model, we theoretically prove and discuss the existence and uniqueness of the Stackelberg equilibrium (SE). Using the proposed iterative algorithm, the optimal solution can be obtained in the optimization problem. The performance of the strategy is shown in the simulation results. It is shown that the simulation results confirm the efficiency of the model in Hetnet.

scholarly journals The Reduction of Initial Reserves Using the Optimal Reinsurance Chains in Non-Life Insurance

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1350
Author(s):  
Galina Horáková ◽  
František Slaninka ◽  
Zsolt Simonka
Keyword(s):  
Life Insurance ◽  
Continuous Time ◽  
Ruin Probability ◽  
Proportional Reinsurance ◽  
Insurance Risk ◽  
Optimal Reinsurance ◽  
Insurance Contracts ◽  
Time Period ◽  
Different Types ◽  
Capital Injections

The aim of the paper is to propose, and give an example of, a strategy for managing insurance risk in continuous time to protect a portfolio of non-life insurance contracts against unwelcome surplus fluctuations. The strategy combines the characteristics of the ruin probability and the values VaR and CVaR. It also proposes an approach for reducing the required initial reserves by means of capital injections when the surplus is tending towards negative values, which, if used, would protect a portfolio of insurance contracts against unwelcome fluctuations of that surplus. The proposed approach enables the insurer to analyse the surplus by developing a number of scenarios for the progress of the surplus for a given reinsurance protection over a particular time period. It allows one to observe the differences in the reduction of risk obtained with different types of reinsurance chains. In addition, one can compare the differences with the results obtained, using optimally chosen parameters for each type of proportional reinsurance making up the reinsurance chain.

scholarly journals A survey of stackelberg differential game models in supply and marketing channels

2008 ◽  
Vol 17 (2) ◽  
pp. 255-255 ◽  
Author(s):  
Xiuli He ◽  
Ashutosh Prasad ◽  
Suresh P. Sethi ◽  
Genaro J. Gutierrez
Keyword(s):  
Differential Game ◽  
Marketing Channels ◽  
Stackelberg Differential Game

Transient analysis of M/M/1 queues in discrete time by general server vacations

1994 ◽  
Vol 31 (A) ◽  
pp. 115-129 ◽  
Author(s):  
W. Böhm ◽  
S. G. Mohanty
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transient Analysis ◽  
Queueing System ◽  
Queueing Model ◽  
Discrete Parameter ◽  
Server Vacations ◽  
Special Case ◽  
Combinatorial Methods ◽  
Transient And Steady State

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

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