scholarly journals An evolutionary monotone follower problem in [0, 1]

1989 ◽  
Vol 31 (1) ◽  
pp. 97-107 ◽  
Author(s):  
Min Sun
Keyword(s):  
Dynamic Programming ◽  
Value Function ◽  
Diffusion Processes ◽  
Control Action ◽  
Integral Type ◽  
Cost Functional ◽  
Controlled Diffusion ◽  
The Cost ◽  
The Value Function ◽  
Controlled Diffusion Processes

AbstractWe consider in this article an evolutionary monotone follower problem in [0,1]. State processes under consideration are controlled diffusion processes , solutions of dyx(t) = g(yx(t), t)dt + σu(yx(t), t) dwt + dυt with yx(0) = x ∈[0, 1], where the control processes υt are increasing, positive, and adapted. The cost functional is of integral type, with certain explicit cost of control action including the cost of jumps. We shall present some analytic results of the value function, mainly its characterisation, by standard dynamic programming arguments.

On Krylov’s estimates for optional semimartingales

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
M. Abdelghani ◽  
A. Melnikov ◽  
A. Pak
Keyword(s):  
Sobolev Space ◽  
Measurable Function ◽  
Diffusion Processes ◽  
Stochastic Integrals ◽  
Controlled Diffusion ◽  
Convergence Of Solutions ◽  
Change Of Variables ◽  
General Class Of Functions ◽  
Class Of Functions ◽  
Controlled Diffusion Processes

Abstract The estimates of N. V. Krylov for distributions of stochastic integrals by means of the L d {L_{d}} -norm of a measurable function are well-known and are widely used in the theory of stochastic differential equations and controlled diffusion processes. We generalize estimates of this type for optional semimartingales, then apply these estimates to prove the change of variables formula for a general class of functions from the Sobolev space W d 2 {W^{2}_{d}} . We also show how to use these estimates for the investigation of L 2 {L^{2}} -convergence of solutions of optional SDE’s.

scholarly journals EVOLUTION OF AMERICAN OPTION VALUE FUNCTION ON A DIVIDEND PAYING STOCK UNDER JUMP-DIFFUSION PROCESSES

2017 ◽  
Vol 2 (3) ◽  
pp. 212-221
Author(s):  
Рехман ◽  
Nazir Rekhman ◽  
Хуссейн ◽  
Zakir Khusseyn ◽  
Али ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Value Function ◽  
Diffusion Processes ◽  
Equivalent Form ◽  
Jump Diffusion ◽  
American Option ◽  
Option Value ◽  
Jump Diffusion Processes ◽  
Hedging Strategies ◽  
The Value Function

This work is devoted to the analysis and evolution of the value function of American type options on a dividend paying stock under jump diffusion processes. An equivalent form of the value function is obtained and analyzed. Moreover, variational inequalities satisfied by this function are investigated. These results can be used to investigate the optimal hedging strategies and optimal exercise boundaries of the corresponding options.

Adaptive Learning of Drug Quality and Optimization of Patient Recruitment for Clinical Trials with Dropouts

2021 ◽  
Author(s):  
Zhili Tian ◽  
Weidong Han ◽  
Warren B. Powell
Keyword(s):  
Clinical Trial ◽  
Clinical Trials ◽  
Dynamic Programming ◽  
Value Function ◽  
Standard Treatment ◽  
Treatment Effectiveness ◽  
Interim Analyses ◽  
Clinical Trial Program ◽  
Patient Enrollment ◽  
The Value Function

Problem definition: Clinical trials are crucial to new drug development. This study investigates optimal patient enrollment in clinical trials with interim analyses, which are analyses of treatment responses from patients at intermediate points. Our model considers uncertainties in patient enrollment and drug treatment effectiveness. We consider the benefits of completing a trial early and the cost of accelerating a trial by maximizing the net present value of drug cumulative profit. Academic/practical relevance: Clinical trials frequently account for the largest cost in drug development, and patient enrollment is an important problem in trial management. Our study develops a dynamic program, accurately capturing the dynamics of the problem, to optimize patient enrollment while learning the treatment effectiveness of an investigated drug. Methodology: The model explicitly captures both the physical state (enrolled patients) and belief states about the effectiveness of the investigated drug and a standard treatment drug. Using Bayesian updates and dynamic programming, we establish monotonicity of the value function in state variables and characterize an optimal enrollment policy. We also introduce, for the first time, the use of backward approximate dynamic programming (ADP) for this problem class. We illustrate the findings using a clinical trial program from a leading firm. Our study performs sensitivity analyses of the input parameters on the optimal enrollment policy. Results: The value function is monotonic in cumulative patient enrollment and the average responses of treatment for the investigated drug and standard treatment drug. The optimal enrollment policy is nondecreasing in the average response from patients using the investigated drug and is nonincreasing in cumulative patient enrollment in periods between two successive interim analyses. The forward ADP algorithm (or backward ADP algorithm) exploiting the monotonicity of the value function reduced the run time from 1.5 months using the exact method to a day (or 20 minutes) within 4% of the exact method. Through an application to a leading firm’s clinical trial program, the study demonstrates that the firm can have a sizable gain of drug profit following the optimal policy that our model provides. Managerial implications: We developed a new model for improving the management of clinical trials. Our study provides insights of an optimal policy and insights into the sensitivity of value function to the dropout rate and prior probability distribution. A firm can have a sizable gain in the drug’s profit by managing its trials using the optimal policies and the properties of value function. We illustrated that firms can use the ADP algorithms to develop their patient enrollment strategies.

2 D amorphous frameworks of NiMoO4 for supercapacitors: defining the role of surface and bulk controlled diffusion processes

2015 ◽  
Vol 326 ◽  
pp. 39-47 ◽  
Author(s):  
Amrutha Ajay ◽  
Anjali Paravannoor ◽  
Jickson Joseph ◽  
Amruthalakshmi V ◽  
Anoop SS ◽  
...  
Keyword(s):  
Diffusion Processes ◽  
Controlled Diffusion ◽  
Controlled Diffusion Processes
Sign in / Sign up

Export Citation Format

Share Document