scholarly journals Modeling Random Fuzzy Renewal Reward Processes

2008 ◽  
Vol 16 (5) ◽  
pp. 1379-1385 ◽  
Author(s):  
Qiang Shen ◽  
Ruiqing Zhao ◽  
Wansheng Tang
Keyword(s):  
Renewal Reward Processes

Sample quantiles of additive renewal reward processes

1996 ◽  
Vol 33 (04) ◽  
pp. 1018-1032 ◽  
Author(s):  
Angelos Dassios
Keyword(s):  
Brownian Motion ◽  
Random Processes ◽  
Independent Increments ◽  
Look Back ◽  
Renewal Reward Processes ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Sample Quantiles

The distribution of the sample quantiles of random processes is important for the pricing of some of the so-called financial ‘look-back' options. In this paper a representation of the distribution of the α-quantile of an additive renewal reward process is obtained as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for processes with stationary and independent increments. As an example, the distribution of the α-quantile of a randomly observed Brownian motion is obtained.

Policy Improvement and the Newton–Raphson Algorithm for Renewal Reward Processes

1989 ◽  
Vol 3 (3) ◽  
pp. 393-396 ◽  
Author(s):  
J. M. McNamara
Keyword(s):  
Continuous Time ◽  
Successive Approximations ◽  
Average Reward ◽  
Policy Improvement ◽  
Unique Root ◽  
Renewal Reward Processes ◽  
Reward Process ◽  
Newton Raphson ◽  
Renewal Reward Process ◽  
Raphson Algorithm

We consider a renewal reward process in continuous time. The supremum average reward, γ* for this process can be characterised as the unique root of a certain function. We show how one can apply the Newton–Raphson algorithm to obtain successive approximations to γ*, and show that the successive approximations so obtained are the same as those obtained by using the policy improvement technique.

Sample quantiles of additive renewal reward processes

1996 ◽  
Vol 33 (4) ◽  
pp. 1018-1032 ◽  
Author(s):  
Angelos Dassios
Keyword(s):  
Brownian Motion ◽  
Random Processes ◽  
Independent Increments ◽  
Look Back ◽  
Renewal Reward Processes ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Sample Quantiles

The distribution of the sample quantiles of random processes is important for the pricing of some of the so-called financial ‘look-back' options. In this paper a representation of the distribution of the α-quantile of an additive renewal reward process is obtained as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for processes with stationary and independent increments. As an example, the distribution of the α-quantile of a randomly observed Brownian motion is obtained.

STOCHASTIC OPTIMAL CONTROL OF ATO SYSTEMS WITH BATCH ARRIVALS VIA DIFFUSION APPROXIMATION

2007 ◽  
Vol 21 (3) ◽  
pp. 477-495 ◽  
Author(s):  
Wanyang Dai ◽  
Qian Jiang
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Heavy Traffic ◽  
Infinite Horizon ◽  
Order System ◽  
Planning Problem ◽  
Batch Arrivals ◽  
Renewal Reward Processes ◽  
Sequencing Rule ◽  
Static Planning

We study the stochastic optimal control for an assemble-to-order system with multiple products and components that arrive at the system in random batches and according to renewal reward processes. Our purpose is to maximize expected infinite-horizon discounted profit by selecting product prices, component production rates, and a dynamic sequencing rule for assembly. We refine the solution of some static planning problem and a discrete review policy to batch arrival environment and develop an asymptotically optimal policy for the system operating under heavy traffic, which indicates that the system can be approximated by a diffusion process and exhibits a state space collapse property.

RENEWAL REWARD PROCESSES

1969 ◽  
Author(s):  
Mark Brown ◽  
Sheldon M. Ross
Keyword(s):  
Renewal Reward Processes
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