On Impulse Control with Partial Observation

Mazziotto, G.; Stettner, Łukasz; Szpirglas, J.; Zabczyk, Jerzy

doi:10.1137/0326052

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…The functional to be minimized has classical form, but the moment of stopping is subject to be a stopping time with respect to the filtration (Y 0 t ) generated by Y , i.e., it has to be based only on the observed process. We follow the classical approach to first solve an optimal stopping problem for the filtering process Π, appropriately formulated and with complete observation, and then to show how this gives a solution to the original problem: see for instance [16] and the references therein for this approach in a general framework. Once more the theory of PDPs turns out to be a very useful tool here, since the existence of an optimal stopping time for Π, as well as a characterization of the value function and the stopping rule, are a direct application of known results on PDPs.…”

Section: Introductionmentioning

confidence: 99%

Filtering of continuous-time Markov chains with noise-free observation and applications

Confortola

Fuhrman

2012

Stochastics

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Let X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set, and let Y be defined by Y t = h(X t ), (t ≥ 0). We address the filtering problem for X in terms of the observation Y , which is not directly affected by noise. We write down explicit equations for the filtering process Π tWe show that Π is a Markov process with the Feller property. We also prove that it is a piecewise-deterministic Markov process in the sense of Davis, and we identify its characteristics explicitly. We finally solve an optimal stopping problem for X with partial observation, i.e. where the moment of stopping is required to be a stopping time with respect to (Y 0 t ).Recently, the following different model has been addressed by several authors:

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Section: Introductionmentioning

confidence: 99%

Filtering of continuous-time Markov chains with noise-free observation and applications

Confortola

Fuhrman

2012

Stochastics

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“…Optimal stopping on general Polish space was studied in [15] using discretization approach, and in [1] using parabolic variational inequalities. Optimal stopping on Polish space appears also in particular in the case of stopping with partial observation in [5]. The convergence of a solution of penalty equation to the value function on a general Polish space, proved in this paper is also new.…”

Section: Introductionmentioning

confidence: 87%

On general optimal stopping problems using penalty method

Stettner

2012

Demonstratio Mathematica

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Abstract. In the paper we use penalty method to approximate a number of general stopping problems over finite horizon. We consider optimal stopping of discrete time or right continuous stochastic processes, and show that suitable version of Snell's envelope can by approximated by solutions to penalty equations. Then we study optimal stopping problem for Markov processes on a general Polish space, and again show that the optimal stopping value function can be approximated by a solution to a Markov version of the penalty equation.

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“…Limited results exist for the corresponding optimal stopping problems on Polish spaces, see e.g. [30,29]. In particular, [30] characterize V as the minimal excessive function dominating G in terms of the (Feller) transition semigroups of (π t , Y t ).…”

Section: Continuation Values and Cashflow Functions For Notational Cmentioning

confidence: 99%

“…[30,29]. In particular, [30] characterize V as the minimal excessive function dominating G in terms of the (Feller) transition semigroups of (π t , Y t ). A more direct theory is available when π t ∈ H belongs to a Hilbert space; this will be the case if ξ 0 (and therefore π t for all t) admits a smooth L 2 -density.…”

Section: Continuation Values and Cashflow Functions For Notational Cmentioning

confidence: 99%

A simulation approach to optimal stopping under partial information

Ludkovski

2009

Stochastic Processes and their Applications

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We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional diffusion with correlated noise. Such models where the controller is not fully aware of her environment are of interest in applied probability and financial mathematics. We propose a new approximate numerical algorithm based on the particle filtering and regression Monte Carlo methods. The algorithm maintains a continuous state-space and yields an integrated approach to the filtering and control sub-problems. Our approach is entirely simulation-based and therefore allows for a robust implementation with respect to model specification. We carry out the error analysis of our scheme and illustrate with several computational examples. An extension to discretely observed stochastic volatility models is also considered.Date: October 31, 2018.

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On Impulse Control with Partial Observation

Cited by 6 publications

References 17 publications

Filtering of continuous-time Markov chains with noise-free observation and applications

Filtering of continuous-time Markov chains with noise-free observation and applications

On general optimal stopping problems using penalty method

A simulation approach to optimal stopping under partial information

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