Mean-Variance Hedging Under Partial Information

Mania, Michael; Tevzadze, R.; Toronjadze, T.

doi:10.1137/070700061

Cited by 22 publications

(17 citation statements)

References 24 publications

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“…Similarly, if we assume σ t and ρ t are observable, we immediately have that ψ F t is F η -adapted and θ t = θ t and, thus, μ t is F η -adapted. Conversely, since all conditions of Theorem 2.1 are satisfied, the process V t is the unique bounded strictly positive solution of Equation (21). Note that θ t = θ t and ρ t = ρ t .…”

Section: Corollary 22mentioning

confidence: 93%

Power Utility Maximization Problems Under Partial Information and Information Sufficiency in a Brownian Setting

Santacroce

Sasso

Trivellato

et al. 2015

Stochastic Analysis and Applications

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We consider the problem of expected power utility maximization from terminal wealth in diffusion market models under partial information. After obtaining novel neat expressions for the value-process and for the optimal strategy, the issue of information sufficiency is addressed. In particular, necessary and sufficient conditions that guarantee that the partial information optimal strategy is still optimal when having access to all market information, are provided.

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Section: Corollary 22mentioning

confidence: 93%

Power Utility Maximization Problems Under Partial Information and Information Sufficiency in a Brownian Setting

Santacroce

Sasso

Trivellato

et al. 2015

Stochastic Analysis and Applications

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“…Mania & Tevzadze [13,15] proved (using more general setup) that a solution of the above problem is given by…”

Section: A System Of Bsdes For Mean-variance Hedgingmentioning

confidence: 99%

“…The technique is extended for a partial information setup by Mania et.al. (2008) [15], for utility maximization by Mania & Santacroce (2010) [16], and for MVH problem with general semimartingales by Jeanblanc et.al. (2012) [7].…”

Section: Introductionmentioning

confidence: 99%

Making mean-variance hedging implementable in a partially observable market

Fujii¹,

Takahashi²

2014

Quantitative Finance

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The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literatures treat the MVH problem by the duality method, here we study a system consisting of three BSDEs derived by Mania and Tevzadze (2003) and Mania et.al.(2008) and try to provide more explicit expressions directly implementable by practitioners. Under the Bayesian and Kalman-Bucy frameworks, we find that a relevant BSDE can yield a semi-closed solution via a simple set of ODEs which allow a quick numerical evaluation. This renders remaining problems equivalent to solving European contingent claims under a new forward measure, and it is straightforward to obtain a forward looking non-sequential Monte Carlo simulation scheme. We also give a special example where the hedging position is available in a semi-closed form. For more generic setups, we provide explicit expressions of approximate hedging portfolio by an asymptotic expansion. These analytic expressions not only allow the hedgers to update the hedging positions in real time but also make a direct analysis of the terminal distribution of the hedged portfolio feasible by standard Monte Carlo simulation.We have added a brief note on a stochastic short rate and Interest-Rate Futures to the original version accepted by Quantitative Finance for publication.

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“…under the hypothesis F S ⊆ G. We include the case when the flow of observable events G does not necessarily contain all information on prices of the underlying asset, i.e., when S, as well as R, is not a G-semimartingale in general. Such an approach, in the context of exponential and mean variance hedging, was considered respectively in [14] and [16] (see also [23,4,20] for the mean variance hedging problem under partial information). We show that the initial problem (1) is equivalent to another maximization problem written in terms of the filtered terminal wealth.…”

Section: Introductionmentioning

confidence: 99%

Power utility maximization under partial information: Some convergence results

Covello¹,

Santacroce²

2010

Stochastic Processes and their Applications

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In this paper we consider the power utility maximization problem under partial information in a continuous semimartingale setting. Investors construct their strategies using the available information, which possibly may not even include the observation of the asset prices. Resorting to stochastic filtering, the problem is transformed into an equivalent one, which is formulated in terms of observable processes. The value process, related to the equivalent optimization problem, is then characterized as the unique bounded solution of a semimartingale backward stochastic differential equation (BSDE). This yields a unified characterization for the value process related to the power and exponential utility maximization problems, the latter arising as a particular case. The convergence of the corresponding optimal strategies is obtained by means of BSDEs. Finally, we study some particular cases where the value process admits an explicit expression.

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Mean-Variance Hedging Under Partial Information

Cited by 22 publications

References 24 publications

Power Utility Maximization Problems Under Partial Information and Information Sufficiency in a Brownian Setting

Power Utility Maximization Problems Under Partial Information and Information Sufficiency in a Brownian Setting

Making mean-variance hedging implementable in a partially observable market

Power utility maximization under partial information: Some convergence results

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