Arbitrage and utility maximization in market models with an insider

Chau, Huy N.; Runggaldier, Wolfgang J.; Tankov, Peter

doi:10.1007/s11579-018-0217-4

Cited by 12 publications

(6 citation statements)

References 38 publications

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“…Nowadays, the optimal portfolio problem with non-continuous assets is still an active topic of research, for example in Chau et al. ( 2018 ), they analyse additional gains generated by an initial enlargement via super-hedging, or Bellalah et al. ( 2020 ), that deals with an example related to the Covid-19 crisis.…”

Section: Introductionmentioning

confidence: 99%

“…Finally Wright et al (2018) weakened some assumptions of the latter paper by assuming the Malliavin derivative were in L 2 (dt × d P). Nowadays, the optimal portfolio problem with non-continuous assets is still an active topic of research, for example in Chau et al (2018), they analyse additional gains generated by an initial enlargement via super-hedging, or Bellalah et al (2020), that deals with an example related to the Covid-19 crisis. See also Colaneri et al (2021), where the value of the market price of risk is compared under different information flows.…”

Section: Introductionmentioning

confidence: 99%

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Anticipative information in a Brownian−Poisson market

D’Auria

Salmerón

2022

Ann Oper Res

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The anticipative information refers to some information about future events that may be disclosed in advance. This information may regard, for example, financial assets and their future trends. In our paper, we assume the existence of some anticipative information in a market whose risky asset dynamics evolve according to a Brownian motion and a Poisson process. Using Malliavin calculus and filtration enlargement techniques, we derive the information drift of the mentioned processes and, both in the pure jump case and in the mixed one, we compute the additional expected logarithmic utility. Many examples are shown, where the anticipative information is related to some conditions that the constituent processes or their running maximum may verify, in particular, we show new examples considering Bernoulli random variables.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Anticipative information in a Brownian−Poisson market

D’Auria

Salmerón

2022

Ann Oper Res

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“…A fundamental question in this context is whether the additional information allows for arbitrage profits. We mention the early work by 1 Grorud and Pontier [20], Amendinger et al [4], Imkeller [23] and subsequent work by Hillairet [21], Acciaio et al [1], Aksamit et al [2], Fontana et al [18], Chau et al [9], among athers. In a general setting, the situations where the additional information of an insider is insufficient for obtaining profits of arbitrage in the form of no free lunch with vanishing risk, were characterised in the literature and linked to the so-called (H) hypothesis holding between the asset price filtration and the larger filtration containing the additional information (see Blanchet-Scalliet and Jeanblanc [6] and Coculescu et al [11]).…”

Section: Introductionmentioning

confidence: 98%

Insiders and Their Free Lunches: The Role of Short Positions

Coculescu¹,

Dandapani²

2022

SIAM J. Finan. Math.

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Given a stock price process, we analyse the potential of arbitrage by insiders in a context of short-selling prohibitions. We introduce the notion of minimal supermartingale measure, and we analyse its properties in connection to the minimal martingale measure. In particular, we establish conditions when both fail to exist. These correspond to the case when the insider's information set includes some non null events that are perceived as having null probabilities by the uninformed market investors. These results may have different applications, such as in problems related to the local risk-minimisation for insiders whenever strategies are implemented without short selling.

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“…Amendinger proves in [6] that under Jacod's hypothesis, insider's model is arbitrage free. Many papers deal with arbitrage opportunities under initial or progressive filtration enlargement (see the recent works of Aksamit et al [3], [4], Acciaio et al [1], Choulli et al [2]) and we can cite the work of Chau, Runggaldier and Tankov [22] in an incomplete market. Most of the aforementioned works take shape in continuous-time settings; they are fewer in a discrete one.…”

Section: Introductionmentioning

confidence: 99%

The insider problem in the trinomial model: a discrete-time jump process approach

Halconruy¹

2021

Preprint

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In an incomplete market underpinned by the trinomial model, we consider two investors: an ordinary agent whose decisions are driven by public information and an insider who possesses from the beginning a surplus of information encoded through a random variable for which he or she knows the outcome. Through the definition of an auxiliary model based on a marked binomial process, we handle the trinomial model as a volatility one, and use the stochastic analysis and Malliavin calculus toolboxes available in that context. In particular, we connect the information drift, i.e. the drift to eliminate in order to preserve the martingale property within an initial enlargement of filtration in terms of Malliavin's derivative. We solve explicitly the agent and the insider expected logarithmic utility maximization problems and provide a Ocone-Karatzas type formula for replicable claims. We identify insider's expected additional utility with the Shannon entropy of the extra information, and examine then the existence of arbitrage opportunities for the insider.

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Arbitrage and utility maximization in market models with an insider

Cited by 12 publications

References 38 publications

Anticipative information in a Brownian−Poisson market

Anticipative information in a Brownian−Poisson market

Insiders and Their Free Lunches: The Role of Short Positions

The insider problem in the trinomial model: a discrete-time jump process approach

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