Sequential Monte Carlo methods for diffusion processes

2009 ◽  
Vol 465 (2112) ◽  
pp. 3709-3727 ◽  
Author(s):  
Ajay Jasra ◽  
Arnaud Doucet
Keyword(s):  
Optimal Control ◽  
Monte Carlo ◽  
Option Pricing ◽  
Monte Carlo Methods ◽  
Sequential Monte Carlo ◽  
Diffusion Processes ◽  
Time Discretization ◽  
Initial Condition ◽  
Sequential Monte Carlo Methods ◽  
Low Dimensional

In this paper, we show how to use sequential Monte Carlo methods to compute expectations of functionals of diffusions at a given time and the gradients of these quantities w.r.t. the initial condition of the process. In some cases, via the exact simulation of the diffusion, there is no time discretization error, otherwise the methods use Euler discretization. We illustrate our approach on both high- and low-dimensional problems from optimal control and establish that our approach substantially outperforms standard Monte Carlo methods typically adopted in the literature. The methods developed here are appropriate for solving a certain class of partial differential equations as well as for option pricing and hedging.

On the optimal control of stationary diffusion processes with inaccessible boundaries and no discounting

1971 ◽  
Vol 8 (03) ◽  
pp. 551-560 ◽  
Author(s):  
R. Morton
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Diffusion Processes ◽  
Necessary Conditions ◽  
Optimal Solution ◽  
Multidimensional Case ◽  
Potential Cost ◽  
One Dimensional ◽  
Dynamic Programming Equation ◽  
Stationary Diffusion

Summary Because there are no boundary conditions, extra properties are required in order to identify the correct potential cost function. A solution of the Dynamic Programming equation for one-dimensional processes leads to an optimal solution within a wide class of alternatives (Theorem 1), and is completely optimal if certain conditions are satisfied (Theorem 2). Necessary conditions are also given. Several examples are solved, and some extension to the multidimensional case is shown.

On the optimal control of stationary diffusion processes with inaccessible boundaries and no discounting

1971 ◽  
Vol 8 (3) ◽  
pp. 551-560 ◽  
Author(s):  
R. Morton
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Diffusion Processes ◽  
Necessary Conditions ◽  
Optimal Solution ◽  
Multidimensional Case ◽  
Potential Cost ◽  
One Dimensional ◽  
Dynamic Programming Equation ◽  
Stationary Diffusion

SummaryBecause there are no boundary conditions, extra properties are required in order to identify the correct potential cost function. A solution of the Dynamic Programming equation for one-dimensional processes leads to an optimal solution within a wide class of alternatives (Theorem 1), and is completely optimal if certain conditions are satisfied (Theorem 2). Necessary conditions are also given. Several examples are solved, and some extension to the multidimensional case is shown.

Optimal Control of Diffusion Processes (Vivek S. Borkar)

SIAM Review ◽  
1990 ◽  
Vol 32 (3) ◽  
pp. 503-504
Author(s):  
Wendell H. Fleming
Keyword(s):  
Optimal Control ◽  
Diffusion Processes
Sign in / Sign up

Export Citation Format

Share Document