Shadow price of information in discrete time stochastic optimization

Pennanen, Teemu; Perkkiö, Ari-Pekka

doi:10.1007/s10107-017-1163-2

Cited by 7 publications

(12 citation statements)

References 26 publications

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“…In, e.g., [6,[25][26][27][28] some form of integrability is always assumed, which leads to further technicalities in the proofs; see also [29,30] and the references therein for basic studies on the relations of (conditional) expectations and integrands. The main results in Sect.…”

Section: Connection To Random Set Theorymentioning

confidence: 99%

Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time

Jamneshan¹,

Kupper

Zapata-García

2020

J Optim Theory Appl

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We prove a general existence result in stochastic optimal control in discrete time, where controls, taking values in conditional metric spaces, depend on the current information and past decisions. The general form of the problem lies beyond the scope of standard techniques in stochastic control theory, the main novelty is a formalization in conditional metric space and the use of conditional analysis. We illustrate the existence result by several examples such as wealth-dependent utility maximization under risk constraints and utility maximization with a conditional dimension. We also provide a discussion as to how our methods compare to techniques based on random sets.

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Section: Connection To Random Set Theorymentioning

confidence: 99%

Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time

Jamneshan¹,

Kupper

Zapata-García

2020

J Optim Theory Appl

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“…We consider the Bellman equation in stochastic dynamic programming and we provide a "Bellman-like" equation for the Fenchel conjugates of the value functions. Related works are [17] and [12].…”

Section: Fenchel Conjugates Of Bellman Functionsmentioning

confidence: 99%

“…Now, we provide a "Bellman-like" equation for the Fenchel conjugates of the value functions (see [12] for related considerations).…”

Section: Fenchel Conjugates Of the Bellman Functionsmentioning

confidence: 99%

Fenchel-Moreau Conjugation Inequalities with Three Couplings and Application to Stochastic Bellman Equation

Chancelier¹,

Lara²

2018

Preprint

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Given two couplings between "primal" and "dual" sets, we prove a general implication that relates an inequality involving "primal" sets to a reverse inequality involving the "dual" sets. More precisely, let be given two "primal" sets X, Y and two "dual" sets X ♯ , Y ♯ , together with two coupling functions+ d between the "primal" product set X × Y and the "dual" product set X ♯ × Y ♯ . Then, we consider any bivariate function K : X × Y → [−∞, +∞] and univariate functions f : X → [−∞, +∞] and g : Y → [−∞, +∞], all defined on the "primal" sets. We prove that f (x), where we stress that the Fenchel-Moreau conjugates f c and g −d are not necessarily taken with the same coupling. We study the equality case. We display several applications. We provide a new formula for the Fenchel-Moreau conjugate of a generalized inf-convolution. We obtain formulas with partial Fenchel-Moreau conjugates. Finally, we consider the Bellman equation in stochastic dynamic programming and we provide a "Bellman-like" equation for the Fenchel conjugates of the value functions.

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“…In e.g. [39,41,42,45,47] some form of integrability is always assumed which leads to further technicalities in the proofs, see also [27,33,44] and the references therein for basic studies on the relations of (conditional) expectations and integrands. The main results in Section 2 are established for general utilities which are not necessarily in the form of expected utilities, and no integrability assumptions are required.…”

Section: Connection To Random Set Theorymentioning

confidence: 99%

Parameter-dependent Stochastic Optimal Control in Finite Discrete Time

Jamneshan¹,

Kupper²,

Zapata³

2017

Preprint

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We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a recursively defined forward process. The generality of the problem lies beyond the scope of standard techniques in stochastic control theory such as random sets, normal integrands and measurable selection theory. The main novelty is a formalization in conditional metric space and the use of techniques in conditional analysis. We illustrate the existence result by several examples including wealth-dependent utility maximization under risk constraints with bounded and unbounded wealth-dependent control sets, utility maximization with a measurable dimension, and dynamic risk sharing. Finally, we discuss how conditional analysis relates to random set theory.

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Shadow price of information in discrete time stochastic optimization

Cited by 7 publications

References 26 publications

Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time

Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time

Fenchel-Moreau Conjugation Inequalities with Three Couplings and Application to Stochastic Bellman Equation

Parameter-dependent Stochastic Optimal Control in Finite Discrete Time

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