The Lagrange approach to ergodic control of diffusions with cost constraints

Mendoza-Pérez, Armando F.; Jasso-Fuentes, Héctor; Hernández–Lerma, Onésimo

doi:10.1080/02331934.2012.736992

Cited by 11 publications

(4 citation statements)

References 11 publications

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“…Naturally, we use the Lagrange multiplier approach to treat the expected constraint problem. In the literature, such constrained problems were considered in [9] for general controlled diffusion models. In contrast to their approach, we treat a problem arising in a financial application.…”

Section: Definition 21mentioning

confidence: 99%

“…We consider an expected control constraint in the sense that the expected cost for the position is limited to a fixed upper bound. To the best of our knowledge, such "soft constraint" has not received much attention in stochastic control literature until recently; see for example, [9]. A natural approach for handling such problems is the use of Lagrange multiplier.…”

Section: Introductionmentioning

confidence: 99%

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A Constrained Stochastic Control Problem with Application to an Illiquid Stock Position Build-Up

Lu¹,

Yin²,

Zhang³

et al. 2017

2017 Proceedings of the Conference on Control and Its Applications

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We consider a class of constrained stochastic optimal control problems with applications to an illiquid stock position build-up. Using a geometric Brownian motion model, we allow the drift to be purchase-rate dependent to characterize "price impact" of heavy share accumulation over time. The constraint is the fund availability. That is, the expected fund availability has an upper bound. We use a Lagrange multiplier method to treat the constrained control problem. Because a closed-form solution is virtually impossible to obtained, we develop approximation schemes, which consist of inner and outer approximations. The inner approximation is a numerical procedure for obtaining optimal strategies based on a fixed parameter of the Lagrange multiplier. The outer approximation is a stochastic approximation algorithm for obtaining the optimal Lagrange multiplier. Convergence analysis together with numerical examples are provided.

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Section: Definition 21mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Constrained Stochastic Control Problem with Application to an Illiquid Stock Position Build-Up

Lu¹,

Yin²,

Zhang³

et al. 2017

2017 Proceedings of the Conference on Control and Its Applications

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show abstract

“…The Lagrange technique studied in [23,27] characterized the discounted problem with constraints by means of an equivalent unconstrained problem using the Lagrange multipliers method so that optimality for the unconstrained yield optimality for the original one when a suitable multiplier is selected.…”

mentioning

confidence: 99%

“…[2,3,4] and their references. On the other hand, controlled diffusions with constraints has been studied in [9,10,27,33].…”

mentioning

confidence: 99%

Constrained stochastic differential games with additive structure: Average and discount payoffs

Escobedo-Trujillo¹,

Alaffita-Hernández²,

López-Martínez³

2018

Journal of Dynamics &Amp; Games

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This paper deals with two-person nonzero-sum stochastic differential games (SDGs) with an additive structure, subject to constraints that are additive also. Our main objective is to give conditions for the existence of constrained Nash equilibria for the case of infinite-horizon discounted payoff. This is done by means of the Lagrange multipliers approach combined with dynamic programming arguments. Then, following the vanishing discount approach, the results in the discounted case are used to obtain constrained Nash equilibria in the case of long-run average payoff.

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Building Up an Illiquid Stock Position Subject to Expected Fund Availability: Optimal Controls and Numerical Methods

Lu¹,

Yin

Zhang

et al. 2016

Appl Math Optim

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We consider a class of constrained stochastic optimal control problems with applications to an illiquid stock position build-up. Using a geometric Brownian motion model, we allow the drift to be purchase-rate dependent to characterize "price impact" of heavy share accumulation over time. The constraint is the fund availability. That is, the expected fund availability has an upper bound. We use a Lagrange multiplier method to treat the constrained control problem. Because a closed-form solution is virtually impossible to obtained, we develop approximation schemes, which consist of inner and outer approximations. The inner approximation is a numerical procedure for obtaining optimal strategies based on a fixed parameter of the Lagrange multiplier. The outer approximation is a stochastic approximation algorithm for obtaining the optimal La-grange multiplier. Convergence analysis together with numerical examples are provided.

show abstract

The Lagrange approach to ergodic control of diffusions with cost constraints

Cited by 11 publications

References 11 publications

A Constrained Stochastic Control Problem with Application to an Illiquid Stock Position Build-Up

A Constrained Stochastic Control Problem with Application to an Illiquid Stock Position Build-Up

Constrained stochastic differential games with additive structure: Average and discount payoffs

Building Up an Illiquid Stock Position Subject to Expected Fund Availability: Optimal Controls and Numerical Methods

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