Impulse and absolutely continuous ergodic control of one-dimensional Itô diffusions

نویسندگان

  • Andrew Jack
  • Mihail Zervos
چکیده

We consider a problem that combines impulse control with absolutely continuous control of the drift of a general one-dimensional Itô diffusion. The objective of the control problem is to minimise an ergodic or long-term average criterion that penalises both deviations of the state process from a given nominal point and the use of control effort. Our analysis completely characterises the optimal strategy.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Itô Diffusions, Modified Capacity and Harmonic Measure. Applications to Schrödinger Operators

We observe that some special Itô diffusions are related to scattering properties of a Schrödinger operator on R, d ≥ 2. We introduce Feynman-Kac type formulae for these stochastic processes which lead us to results on the preservation of the a.c. spectrum of the Schrödinger operator. To better understand the analytic properties of the processes, we construct and study a special version of the p...

متن کامل

Discretionary Stopping of One-dimensional Itô Diffusions with a Staircase Reward Function

We consider the problem of optimally stopping a general one-dimensional Itô diffusion X. In particular, we solve the problem that aims at maximising the performance criterion Ex [exp(− ∫ τ 0 r(Xs) ds)f (Xτ )] over all stopping times τ , where the reward function f can take only a finite number of values and has a ‘staircase’ form. This problem is partly motivated by applications to financial as...

متن کامل

Ergodic Potentials with a Discontinuous Sampling Function Are Non-deterministic

We prove absence of absolutely continuous spectrum for discrete one-dimensional Schrödinger operators on the whole line with certain ergodic potentials, Vω(n) = f(T n(ω)), where T is an ergodic transformation acting on a space Ω and f : Ω → R. The key hypothesis, however, is that f is discontinuous. In particular, we are able to settle a conjecture of Aubry and Jitomirskaya–Mandel’shtam regardi...

متن کامل

Ergodic control of diffusion processes

Results concerning existence and characterization of optimal controls for ergodic control of nondegenerate diffusion processes are described. Extensions to the general ‘controlled martingale problem’ are indicated, which cover in particular degenerate diffusions and some infinite dimensional problems. In conclusion, some related problems and open issues are discussed. Mathematics Subject Classi...

متن کامل

Resonances for ”large” ergodic systems in one dimension: a review

The present note reviews recent results on resonances for one-dimensional quantum ergodic systems constrained to a large box. We restrict ourselves to one dimensional models in the discrete case. We consider two type of ergodic potentials on the half-axis, periodic potentials and random potentials. For both models, we describe the behavior of the resonances near the real axis for a large typica...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004