Utility Maximization in a Large Market

Mostovyi, Oleksii

doi:10.1111/mafi.12123

Cited by 8 publications

(9 citation statements)

References 31 publications

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“…Such results are standard for finitely many assets (see the references in [17]), but in the present context we face infinite-dimensional portfolios. In the setting of APT, we mention [20], which relies on the notion of generalized portfolios. Utility functions defined on the real line (i.e., admitting losses) have been considered in [12,13] (we expose the differences between these two papers and ours in Remark 3.2).…”

Section: Introductionmentioning

confidence: 99%

Risk-Neutral Pricing for Arbitrage Pricing Theory

Carassus

Rásonyi

2020

J Optim Theory Appl

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We consider infinite-dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the superreplication cost. Then, we show the existence of optimal strategies for investors maximizing their expected utility and the convergence of their reservation prices to the super-replication cost as their riskaversion tends to infinity.

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Section: Introductionmentioning

confidence: 99%

Risk-Neutral Pricing for Arbitrage Pricing Theory

Carassus

Rásonyi

2020

J Optim Theory Appl

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“…This theory stochastic integration has found applications to mathematical finance, in particular in modelling large markets (see e.g. [7,35]). In the following paragraphs we describe the main ideas in the construction of the stochastic integral introduced in [8].…”

Section: Proposition 64mentioning

confidence: 99%

Stochastic integration with respect to cylindrical semimartingales

Fonseca-Mora

2021

Electron. J. Probab.

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In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space Φ. Our construction of the stochastic integral is based on the theory of tensor products of topological vector spaces and the property of good integrators of real-valued semimartingales. This theory is further developed in the case where Φ is a complete, barrelled, nuclear space, where we obtain a complete description of the class of integrands as Φ-valued locally bounded and weakly predictable processes. Several other properties of the stochastic integral are proven, including a Riemann representation, a stochastic integration by parts formula and a stochastic Fubini theorem. Our theory is then applied to provide sufficient and necessary conditions for existence and uniqueness of solutions to linear stochastic evolution equations driven by semimartingale noise taking values in the strong dual Φ of Φ. In the last part of this article we apply our theory to define stochastic integrals with respect to a sequence of real-valued semimartingales.

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“…Remark 4.8. The only papers in the existing literature that are closely related to ours are [9] and [26], where the expected utility of an investor is maximized in a continuous-time large financial market over a set of "generalized portfolios". The first paper is about maximizing terminal utility while the second paper deals with utility from consumption, allowing random utility functions and a stochastic clock.…”

Section: Corollary 44 Let Assumption 35 Be In Force and Assumementioning

confidence: 99%

“…There has also been a recent revival of interest in such models, see [25,6]. In the context of optimization, [9] and [26] are the only previous studies we are aware of.…”

Section: Introductionmentioning

confidence: 99%