Robust Valuation, Arbitrage Ambiguity and Profit &amp; Loss Analysis

Xu, Yuhong

doi:10.1007/s40305-017-0181-3

Cited by 4 publications

(1 citation statement)

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“…In the recent years the framework of G-expectation has found increasing application in the domain of finance and economics, e.g., Epstein and Ji [17,16] study the asset pricing with ambiguity preferences, Beissner [5] who studies the equilibrium theory with ambiguous volatility, and many others see e.g. [50,6,51], also see [25,26,27].for numerical methods. The motivation is that many systems are subject to model uncertainty or ambiguity due to incomplete information, or vague concepts and principles.…”

Section: Introductionmentioning

confidence: 99%

The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps

Gherbal¹,

Mezerdi²

2017

AJAS

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Abstract. This paper is concerned with optimal control of systems driven by stochastic differential equations (SDEs), with jump processes, where the control variable appears in the drift and in the jump term. We study the relaxed problem, in which admissible controls are measure-valued processes and the state variable is governed by an SDE driven by a counting measure valued process called relaxed Poisson measure such that the compensator is a product measure. Under some conditions on the coefficients, we prove that every diffusion process associated to a relaxed control is a limit of a sequence of diffusion processes associated to strict controls. As a consequence, we show that the strict and the relaxed control problems have the same value function. Using similar arguments, we prove the existence of an optimal relaxed control. In a second step, we establish a maximum principle for this type of relaxed problem.Key words: Stochastic control, Stochastic differential equation, jump process, optimal control, relaxed control -maximum principle. AMS 2010 Mathematics Subject Classification : 93E20, 60H10 Résumé (French Abstract). L'objectif de cet article est l'étude du contrôle optimal de systèmes dirigés par deséquations différentielles stochastiques (EDS), présentant des sauts, où le paramètre de contrôle apparaît aussi bien dans le drift que dans le terme de saut. Nousétudions le problème relaxé, dans lequel les contrôles admissibles sont des processusà valeurs mesures et la variable d'état est gouvernée par une EDS dirigée par une mesure de comptage appelée mesure de Poisson relaxée, dont le compensateur est une mesure produit. Sous certaines hypothèses sur les coefficients, nous montrons que tout processus de diffusion * Corresponding author Brahim Mezerdi : bmezerdi@yahoo.fr Ben Gherbal Hanane : hananebengherbal@yahoo.fr B. G. Hanane and B. Mezerdi, Afrika Statistika, Vol. 12 (2), 2017, 1287 -1312. The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps. 1288associéà un contrôle relaxé est limite d'une suite de diffusions associéesà des contrôles stricts. Comme conséquence, nousétablissons que les problèmes de contrôle strict et relaxé ont la même fonction de valeurs. En utilisant des arguments similaires, nous montrons l'existence d'un contrôle optimal relaxé. Dans une deuxièmeétape, nous démontrons un principe du maximum pour ce type de problème relaxé.

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Section: Introductionmentioning

confidence: 99%

The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps

Gherbal¹,

Mezerdi²

2017

AJAS

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Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps

Redjil

Gherbal

Kebiri

2021

Stochastic Analysis and Applications

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Volatility Ambiguity, Portfolio Decisions, and Equilibrium Asset Pricing

Liu,

Wang,

Wang

et al. 2024

Management Science

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This paper develops a new approach to volatility ambiguity and studies its implications for equilibrium consumption, portfolio choice, and asset prices. Our approach does not require equivalence between priors. The measure of ambiguity is based on the statistical confidence in the reference model that can be assessed with sample statistics. The approach is analytically tractable and amenable to empirical/calibration analysis. A stochastic discount pricing formula is given. At sensible levels of volatility ambiguity, the empirical regularity of equity premium and consumption growth in U.S. data can be the equilibrium outcome of our model featuring a relative risk aversion (RRA) coefficient within a reasonable range. This paper was accepted by Will Cong, finance. Funding: H. Wang received financial support from the Tsinghua University Initiative Scientific Research Program [2023THZWJC20]. L. Zhang received financial support from the Tsinghua University Initiative Scientific Research Program [2021THZWJC28] and The National Natural Science Foundation of China [Grant 72473079]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.02902 .

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Robust Valuation, Arbitrage Ambiguity and Profit & Loss Analysis

Cited by 4 publications

References 46 publications

The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps

The relaxed stochastic maximum principle in optimal control of diffusions with controlled jumps

Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps

Volatility Ambiguity, Portfolio Decisions, and Equilibrium Asset Pricing

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