Jati K. Sengupta (auth.)'s Stochastic Optimization and Economic Models PDF

By Jati K. Sengupta (auth.)

ISBN-10: 9048184266

ISBN-13: 9789048184262

ISBN-10: 9401730857

ISBN-13: 9789401730853

This ebook offers the most utilized elements of stochas­ tic optimization in financial versions. Stochastic strategies and keep watch over thought are used less than optimization to demonstrate a few of the monetary implications of optimum selection principles. in contrast to econometrics which offers with estimation, this ebook emphasizes the decision-theoretic foundation of uncertainty laid out in the stochastic perspective. equipment of ap­ plied stochastic regulate utilizing stochastic procedures have now reached an exciti~g part, the place numerous disciplines like platforms engineering, operations learn and normal reso- ces engage in addition to the normal fields equivalent to mathematical economics, finance and keep an eye on platforms. Our goal is to give a serious evaluate of this huge terrain from a multidisciplinary point of view. during this try out we've got every now and then under pressure viewpoints except the merely fiscal one. We think that the economist may locate it such a lot ecocnomic to benefit from the opposite disciplines the place stochastic optimization has been effectively utilized. it truly is during this spirit that we've got mentioned in a few aspect the subsequent significant parts: A. Portfolio versions in ·:finance, B. Differential video games less than uncertainty, c. Self-tuning regulators, D. types of renewable assets below uncertainty, and ix x PREFACE E. Nonparametric equipment of potency size. Stochastic methods at the moment are more and more utilized in monetary versions to appreciate some of the adaptive habit implicit within the formula of expectation and its program in selection ideas that are optimal in a few sense.

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1 , g . ' g~'+ 1 , ... 4) for all i=l,2, .. , n In other words, the strategies g~ 1 specifies the best response of player i (i=1,2, .. s .... , gt_ , ... , 1 g~) of the other n-1 players. Now we introduce the functions hi(x,t) = (h (x,t), .... , hi_ (x,t), hi+ (x,t), ... , continuity and boundedness). Then player i solves the optimal decision problem as: max J. u. 5) 1 Let {ui(t)JO~t~T} be the optimal solution trajectory, when it exists. 5). Thus if the time path of the state variable x(t) is available (or expected), then the player i can easily construct the expected time path of control (u (t), u {t), ...

Conjectural variations and the perceived influence of each player on the market. Yet it is clear that in a stochastic environment of future demand and potential entry, these two factors may play a crucial role. We consider a few formulations in this regard. A dynamic formulation of conjectural equilibrium which leads in its steady state to a Cournot solution is due to Kamien and Schwartz [5] and Fershtman and Kamien [6]. They consider a dynamic market as x = f(x,u,t), x(O) = x0 ( 1. 1) with x and u as the state and control vectors and a dot denotes the time derivative.

3. Illustrative Applications We may now consider some examples of application of selected stochastic processes to economics and other operational fields. These examples illustrate the following problems in stochastic processes and control: A. Optimal control of a queuing process, B. Stochastic control as Kalman filter problem, C. Optimal extraction of a natural resource under demand uncertainty, D. Problems of optimal search, and E. Stability of stochastic systems satisfying dynamic random equations.

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Stochastic Optimization and Economic Models by Jati K. Sengupta (auth.)


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