Markov control processes with randomized discounted cost

González-Hernández, Juan; López-Martínez, Raquiel R.; Pérez-Hernández, J. Rubén

doi:10.1007/s00186-006-0092-2

Cited by 21 publications

(14 citation statements)

References 25 publications

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“…As for the area of personal finance planning, there are articles concerning the lifetime wealth allocation between consumption and investment in a multi-period window (e.g. Schied, 2008;González-Hernández et al, 2007;Gupta and Li, 2007;Chen and Yuen, 2005;Chen and Milevsky, 2003;Vigna and Haberman, 2001;Brown, 1987). However, the role and impact of taxation is not directly discussed in these models.…”

Section: Literature Reviewmentioning

confidence: 99%

Decision model and analysis for investment interest expense deduction and allocation

Lee

Deng

Lin

et al. 2010

European Journal of Operational Research

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Section: Literature Reviewmentioning

confidence: 99%

Decision model and analysis for investment interest expense deduction and allocation

Lee

Deng

Lin

et al. 2010

European Journal of Operational Research

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“…Recently, in Wei and Guo (2011), some results in Schäl (1975) were extended to the unbounded cost case considering state-dependent discount factors. On the other hand, randomized discounted criteria have been analyzed in González-Hernández et al (2007, 2008, 2013, 2014 addressing several issues: existence of optimal strategies, adaptive control, approximation algorithms, and problems with constraints. In these cases, the discount factor is modeled as a stochastic process, independent of the state-action pairs, which is defined in terms of a suitable discrete-time Markov process.…”

Section: Introductionmentioning

confidence: 99%

Markov control models with unknown random state–action-dependent discount factors

Minjárez‐Sosa

2015

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The paper deals with a class of discounted discrete-time Markov control models with non-constant discount factors of the formα(x n , a n , ξ n+1 ), where x n , a n , and ξ n+1 are the state, the action, and a random disturbance at time n, respectively, taking values in Borel spaces. Assuming that the one-stage cost is possibly unbounded and that the distributions of ξ n are unknown, we study the corresponding optimal control problem under two settings. Firstly we assume that the random disturbance process {ξ n } is formed by observable independent and identically distributed random variables, and then we introduce an estimation and control procedure to construct strategies. Instead, in the second one, {ξ n } is assumed to be non-observable whose distributions may change from stage to stage, and in this case the problem is studied as a minimax control problem in which the controller has an opponent selecting the distribution of the corresponding random disturbance at each stage.

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“…González-Hernández et al [12] assume MCMs where the discount factor has an exponential form and the discount rate is modelled as a non-negative Markov chain {r n : n ∈ N} over (0, ∞) :…”

Section: Introductionmentioning

confidence: 99%