Publisher's Synopsis
Stochastic modeling and control play an important role in various scientific and applied disciplines with communications, engineering, medicine, finance and many others. Stochastic control refers to the general area in which some random variable distributions depend on the choice of certain controls, and one looks for an optimal strategy to choose those controls in order to maximize or minimize the expected value of the random variable. The random variable to optimize is computed in terms of some stochastic process. It is usually the value of some given function evaluated at the end point of the stochastic process. Mathematical models, be they deterministic or stochastic, are intended to mimic real world systems. In particular, they can be used to predict how systems will behave under specified conditions. In scientific work, we may be able to conduct experiments to see if model predictions agree with what actually happens in practice. But in many situations, experimentation is impossible. Even if experimentation is conceivable in principle, it may be impractical for ethical or financial reasons. In these circumstances, the model can only be tested less formally, for example by seeking expert opinion on the predictions of the model. In a continuous time approach in a finance context, the state variable in the stochastic differential equation is usually wealth or net worth, and the controls are the shares placed at each time in the various assets. Given the asset allocation chosen at any time, the determinants of the change in wealth are usually the stochastic returns to assets and the interest rate on the risk-free asset. The field of stochastic control has developed greatly since the 1970s, particularly in its applications to finance. Robert Merton used stochastic control to study optimal portfolios of safe and risky assets. Stochastic Modeling, Estimation and Control is a compendium of outstanding investigations in numerous aspects of stochastic systems and their behavior. The book provides a self-sufficient treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. This is a concise and elementary introduction to stochastic control and mathematical modelling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Stochastic modeling and control play an important role in various scientific and applied disciplines with communications, engineering, medicine, finance and many others. Stochastic control refers to the general area in which some random variable distributions depend on the choice of certain controls, and one looks for an optimal strategy to choose those controls in order to maximize or minimize the expected value of the random variable. The random variable to optimize is computed in terms of some stochastic process. It is usually the value of some given function evaluated at the end point of the stochastic process. Mathematical models, be they deterministic or stochastic, are intended to mimic real world systems. In particular, they can be used to predict how systems will behave under specified conditions. In scientific work, we may be able to conduct experiments to see if model predictions agree with what actually happens in practice. But in many situations, experimentation is impossible. Even if experimentation is conceivable in principle, it may be impractical for ethical or financial reasons. In these circumstances, the model can only be tested less formally, for example by seeking expert opinion on the predictions of the model. In a continuous time approach in a finance context, the state variable in the stochastic differential equation is usually wealth or net worth, and the controls are the shares placed at each time in the various assets. Given the asset allocation chosen at any time, the determinants of the change in wealth are usually the stochastic returns to assets and the interest rate on the risk-free asset. The field of stochastic control has developed greatly since the 1970s, particularly in its applications to finance. Robert Merton used stochastic control to study optimal portfolios of safe and risky assets. Stochastic Modeling, Estimation and Control is a compendium of outstanding investigations in numerous aspects of stochastic systems and their behavior. The book provides a self-sufficient treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. This is a concise and elementary introduction to stochastic control and mathematical modelling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Stochastic modeling and control play an important role in various scientific and applied disciplines with communications, engineering, medicine, finance and many others. Stochastic control refers to the general area in which some random variable distributions depend on the choice of certain controls, and one looks for an optimal strategy to choose those controls in order to maximize or minimize the expected value of the random variable. The random variable to optimize is computed in terms of some stochastic process. It is usually the value of some given function evaluated at the end point of the stochastic process. Mathematical models, be they deterministic or stochastic, are intended to mimic real world systems. In particular, they can be used to predict how systems will behave under specified conditions. In scientific work, we may be able to conduct experiments to see if model predictions agree with what actually happens in practice. But in many situations, experimentation is impossible. Even if experimentation is conceivable in principle, it may be impractical for ethical or financial reasons. In these circumstances, the model can only be tested less formally, for example by seeking expert opinion on the predictions of the model. In a continuous time approach in a finance context, the state variable in the stochastic differential equation is usually wealth or net worth, and the controls are the shares placed at each time in the various assets. Given the asset allocation chosen at any time, the determinants of the change in wealth are usually the stochastic returns to assets and the interest rate on the risk-free asset. The field of stochastic control has developed greatly since the 1970s, particularly in its applications to finance. Robert Merton used stochastic control to study optimal portfolios of safe and risky assets. Stochastic Modeling, Estimation and Control is a compendium of outstanding investigations in numerous aspects of stochastic systems and their behavior. The book provides a self-sufficient treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. This is a concise and elementary introduction to stochastic control and mathematical modelling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Stochastic modeling and control play an important role in various scientific and applied disciplines with communications, engineering, medicine, finance and many others. Stochastic control refers to the general area in which some random variable distributions depend on the choice of certain controls, and one looks for an optimal strategy to choose those controls in order to maximize or minimize the expected value of the random variable. The random variable to optimize is computed in terms of some stochastic process. It is usually the value of some given function evaluated at the end point of the stochastic process. Mathematical models, be they deterministic or stochastic, are intended to mimic real world systems. In particular, they can be used to predict how systems will behave under specified conditions. In scientific work, we may be able to conduct experiments to see if model predictions agree with what actually happens in practice. But in many situations, experimentation is impossible. Even if experimentation is conceivable in principle, it may be impractical for ethical or financial reasons. In these circumstances, the model can only be tested less formally, for example by seeking expert opinion on the predictions of the model. In a continuous time approach in a finance context, the state variable in the stochastic differential equation is usually wealth or net worth, and the controls are the shares placed at each time in the various assets. Given the asset allocation chosen at any time, the determinants of the change in wealth are usually the stochastic returns to assets and the interest rate on the risk-free asset. The field of stochastic control has developed greatly since the 1970s, particularly in its applications to finance. Robert Merton used stochastic control to study optimal portfolios of safe and risky assets. Stochastic Modeling, Estimation and Control is a compendium of outstanding investigations in numerous aspects of stochastic systems and their behavior. The book provides a self-sufficient treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, s
