scholarly journals Correction to ``The value function in ergodic control of diffusion processes with partial observations II" (Applicationes Math. 27 (2000), 455–464)

2001 ◽  
Vol 28 (2) ◽  
pp. 245-246 ◽  
Author(s):  
V. S. Borkar
Keyword(s):  
Value Function ◽  
Diffusion Processes ◽  
Ergodic Control ◽  
Partial Observations ◽  
The Value Function

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.

scholarly journals The First Passage Time and the Dividend Value Function for One-Dimensional Diffusion Processes between Two Reflecting Barriers

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Chuancun Yin ◽  
Huiqing Wang
Keyword(s):  
Boundary Conditions ◽  
Value Function ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
The Laplace Transform ◽  
The Value Function ◽  
Reflecting Barriers

We consider the general one-dimensional time-homogeneous regular diffusion process between two reflecting barriers. An approach based on the Itô formula with corresponding boundary conditions allows us to derive the differential equations with boundary conditions for the Laplace transform of the first passage time and the value function. As examples, the explicit solutions of them for several popular diffusions are obtained. In addition, some applications to risk theory are considered.

scholarly journals Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs

2007 ◽  
Vol 39 (3) ◽  
pp. 669-689 ◽  
Author(s):  
Jostein Paulsen
Keyword(s):  
Optimal Policy ◽  
Value Function ◽  
Diffusion Processes ◽  
Fixed Cost ◽  
Model Parameters ◽  
Dividend Payment ◽  
Optimal Dividends ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
The Value Function

The problem of optimal dividends paid until absorbtion at zero is considered for a rather general diffusion model. With each dividend payment there is a proportional cost and a fixed cost. It is shown that there can be essentially three different solutions depending on the model parameters and the costs. (i) Whenever assets reach a barrier y*, they are reduced to y* - δ* through a dividend payment, and the process continues. (ii) Whenever assets reach a barrier y*, everything is paid out as dividends and the process terminates. (iii) There is no optimal policy, but the value function is approximated by policies of one of the two above forms for increasing barriers. A method to numerically find the optimal policy (if it exists) is presented and numerical examples are given.

THE VALUATION OF RUSSIAN OPTIONS FOR DOUBLE EXPONENTIAL JUMP DIFFUSION PROCESSES

2010 ◽  
Vol 27 (02) ◽  
pp. 227-242 ◽  
Author(s):  
ATSUO SUZUKI ◽  
KATSUSHIGE SAWAKI
Keyword(s):  
Value Function ◽  
Diffusion Processes ◽  
Closed Form Solution ◽  
Jump Diffusion ◽  
Form Solution ◽  
Jump Diffusion Processes ◽  
Double Exponential ◽  
Analytical Properties ◽  
Russian Option ◽  
The Value Function

In this paper, we derive closed form solution for Russian option with jumps. First, we discuss the pricing of Russian options when the stock pays dividends continuously. Secondly, we derive the value function of Russian options by solving the ordinary differential equation with some conditions (the value function is continuous and differentiable at the optimal boundary for the buyer). And we investigate properties of optimal boundaries of the buyer. Finally, some numerical results are presented to demonstrate analytical properties of the value function.

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.

scholarly journals Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs

2007 ◽  
Vol 39 (03) ◽  
pp. 669-689 ◽  
Author(s):  
Jostein Paulsen
Keyword(s):  
Optimal Policy ◽  
Value Function ◽  
Diffusion Processes ◽  
Fixed Cost ◽  
Model Parameters ◽  
Dividend Payment ◽  
Optimal Dividends ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
The Value Function

The problem of optimal dividends paid until absorbtion at zero is considered for a rather general diffusion model. With each dividend payment there is a proportional cost and a fixed cost. It is shown that there can be essentially three different solutions depending on the model parameters and the costs. (i) Whenever assets reach a barrier y *, they are reduced to y * - δ* through a dividend payment, and the process continues. (ii) Whenever assets reach a barrier y *, everything is paid out as dividends and the process terminates. (iii) There is no optimal policy, but the value function is approximated by policies of one of the two above forms for increasing barriers. A method to numerically find the optimal policy (if it exists) is presented and numerical examples are given.

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):  
Назир Рехман ◽  
Nazir Rekhman ◽  
Закир Хуссейн ◽  
Zakir Khusseyn ◽  
Файха 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.

Ergodic Control of Diffusion Processes

2009 ◽  
Author(s):  
Ari Arapostathis ◽  
Vivek S. Borkar ◽  
Mrinal K. Ghosh
Keyword(s):  
Diffusion Processes ◽  
Ergodic Control
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