Linear-quadratic generalized Stackelberg games with jump-diffusion processes and related forward-backward stochastic differential equations

2021 ◽  
Author(s):  
Na Li ◽  
Jie Xiong ◽  
Zhiyong Yu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Backward Stochastic Differential Equations ◽  
Stackelberg Games ◽  
Linear Quadratic ◽  
Jump Diffusion Processes

AN ERGODIC BSDE RISK REPRESENTATION IN A JUMP-DIFFUSION FRAMEWORK

2021 ◽  
pp. 2150015
Author(s):  
CALISTO GUAMBE ◽  
LESEDI MABITSELA ◽  
RODWELL KUFAKUNESU
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Risk Measures ◽  
Risk Measure ◽  
Jump Diffusion ◽  
Backward Stochastic Differential Equations ◽  
Financial Position ◽  
Entropic Risk Measure ◽  
Risk Representation

We consider the representation of forward entropic risk measures using the theory of ergodic backward stochastic differential equations in a jump-diffusion framework. Our paper can be viewed as an extension of the work considered by Chong et al. (2019) in the diffusion case. We also study the behavior of a forward entropic risk measure under jumps when a financial position is held for a longer maturity.

Optimal insurance control for insurers with jump-diffusion risk processes

2018 ◽  
Vol 13 (1) ◽  
pp. 198-213
Author(s):  
Linlin Tian ◽  
Lihua Bai
Keyword(s):  
Diffusion Processes ◽  
Compound Poisson Process ◽  
Linear Quadratic Regulator ◽  
Jump Diffusion ◽  
Analytic Solutions ◽  
Linear Quadratic ◽  
Discounted Cost ◽  
Optimal Insurance ◽  
Jump Diffusion Processes ◽  
Risk Processes

AbstractIn this paper, we model the surplus process as a compound Poisson process perturbed by diffusion and allow the insurer to ask its customers for input to minimize the distance from some prescribed target path and the total discounted cost on a fixed interval. The problem is reduced to a version of a linear quadratic regulator under jump-diffusion processes. It is treated using three methods: dynamic programming, completion of square and the stochastic maximum principle. The analytic solutions to the optimal control and the corresponding optimal value function are obtained.

scholarly journals Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Li Chen ◽  
Zhen Wu ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Delay System ◽  
Linear Quadratic ◽  
Stochastic Linear System ◽  
And Control

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

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