Abstract
In the financial engineering field, many problems can be formulated as stochastic control problems. A unique feature of the stochastic control problem is that uncertain factors are involved in the evolution of the controlled system and thus the objective function in the stochastic control is typically formed by an expectation operator. There are in general two approaches to solve this kind of problems. One can reformulate the problem to be a deterministic problem and solve the corresponding partial differential equation. Alternatively, one calculates conditional expectations occurring in the problem by either numerical integration orMonte Carlo methods.
We focus on solving various types ofmultiperiod stochastic control problems via the Monte Carlo approach. We employ the Bellman dynamic programming principle so that a multiperiod control problem can be transformed into a composition of several singleperiod control problems, that can be solved recursively. For each singleperiod control problem, conditional expectations with different filtrations need to be calculated. In order to avoid nested simulation (i.e. Monte Carlo simulation within aMonte Carlo simulation), which may be very time consuming, we implement Monte Carlo simulation and crosspath leastsquares regression. Socalled “regresslater” and “bundling” approaches are introduced in our algorithms to make them highly accurate and robust. In most cases, high quality results can be obtained within seconds.
We focus on solving various types ofmultiperiod stochastic control problems via the Monte Carlo approach. We employ the Bellman dynamic programming principle so that a multiperiod control problem can be transformed into a composition of several singleperiod control problems, that can be solved recursively. For each singleperiod control problem, conditional expectations with different filtrations need to be calculated. In order to avoid nested simulation (i.e. Monte Carlo simulation within aMonte Carlo simulation), which may be very time consuming, we implement Monte Carlo simulation and crosspath leastsquares regression. Socalled “regresslater” and “bundling” approaches are introduced in our algorithms to make them highly accurate and robust. In most cases, high quality results can be obtained within seconds.
Original language  English 

Supervisors/Advisors 

Award date  19 Dec 2016 
Print ISBNs  9789461867537 
DOIs  
Publication status  Published  2016 
Keywords
 Stochastic optimization
 portfolio management
 Monte Carlo simulations
 least squares regression