scholarly journals Fluid Limits of Optimally Controlled Queueing Networks

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Guodong Pang ◽  
Martin V. Day
Keyword(s):  
Control Problem ◽  
Queueing Networks ◽  
Value Functions ◽  
Fluid Limit ◽  
Skorokhod Problem ◽  
Optimal Value ◽  
Deterministic Control ◽  
Queueing Processes ◽  
Optimal Value Functions ◽  
Discounted Control Problem

We consider a class of queueing processes represented by a Skorokhod problem coupled with a controlled point process. Posing a discounted control problem for such processes, we show that the optimal value functions converge, in the fluid limit, to the value of an analogous deterministic control problem for fluid processes.

scholarly journals Optimal Reinsurance Strategy for an Insurer and a Reinsurer with Generalized Variance Premium Principle

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Danping Li ◽  
Chaohai Shen
Keyword(s):  
Regularization Parameter ◽  
Risk Process ◽  
Model Parameters ◽  
Value Functions ◽  
Optimal Reinsurance ◽  
Terminal Wealth ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
Optimal Value Functions

This paper focuses on the optimal reinsurance problem with consideration of joint interests of an insurer and a reinsurer. In our model, the risk process is assumed to follow a Brownian motion with drift. The insurer can transfer the risk to the reinsurer via proportional reinsurance, and the reinsurance premium is calculated according to the variance and standard deviation premium principles. The objective is to maximize the expected exponential utility of the weighted sum of the insurer’s and the reinsurer’s terminal wealth, where the weight can be viewed as a regularization parameter to measure the importance of each party. By applying stochastic control theory, we establish the Hamilton–Jacobi–Bellman equation and obtain explicit expressions of optimal reinsurance strategies and optimal value functions. Furthermore, we provide some numerical simulations to illustrate the effects of model parameters on the optimal reinsurance strategies.

Dynamic admission control for loss systems with batch arrivals

2005 ◽  
Vol 37 (04) ◽  
pp. 915-937 ◽  
Author(s):  
E. L. Örmeci ◽  
A. Burnetas
Keyword(s):  
Admission Control ◽  
Sufficient Conditions ◽  
Monotonicity Property ◽  
Value Functions ◽  
Single Class ◽  
Batch Arrivals ◽  
Optimal Value ◽  
Service Rates ◽  
Definition Of ◽  
Optimal Value Functions

We consider the problem of dynamic admission control in a Markovian loss system with two classes. Jobs arrive at the system in batches; each admitted job requires different service rates and brings different revenues depending on its class. We introduce the definition of a ‘preferred class’ for systems receiving mixed and single-class batches separately, and derive sufficient conditions for each system to have a preferred class. We also establish a monotonicity property of the optimal value functions, which reduces the number of possibly optimal actions.

Sign in / Sign up

Export Citation Format

Share Document