Optimal investment with inside information and parameter uncertainty

Danilova, Albina; Monoyios, Michael; Ng, Andrew

doi:10.1007/s11579-010-0025-y

Cited by 27 publications

(25 citation statements)

References 32 publications

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“…. , d}, (V i t ) t∈[0,T ] is a deterministic process, continuous 12 and bounded, modelling the market volume for the i th risky asset, 13 and where (L i ) 1≤i≤d model execution costs. For each i ∈ {1, .…”

Section: Almgren-chris Modelling Framework and Optimization Problemsmentioning

confidence: 99%

Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

Bismuth

Guéant

Pu³

2019

Math Finan Econ

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This paper presents several models addressing optimal portfolio choice, optimal portfolio liquidation, and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling between Bayesian learning and dynamic programming techniques that leads to partial differential equations. It enables to recover the well-known results of Karatzas and Zhao in a framework à la Merton, but also to deal with cases where martingale methods are no longer available. In particular, we address optimal portfolio choice, portfolio liquidation, and portfolio transition problems in a framework à la Almgren-Chriss, and we build therefore a model in which the agent takes into account in his decision process both the liquidity of assets and the uncertainty with respect to their expected return.

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Section: Almgren-chris Modelling Framework and Optimization Problemsmentioning

confidence: 99%

Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

Bismuth

Guéant

Pu³

2019

Math Finan Econ

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“…We refer the reader to Danilova, Monoyios and Ng [3] for further examples, such as when the additional information involves noisy knowledge of the terminal stock price. The work in this section and in [3] extends the classical inside information model of Pikovsky and Karatzas [29] by considering the situation where the insider does not know the stock's appreciation rate. The agent must use strategies that are adapted to the stock price filtration, but enlarged by the additional information.…”

Section: Investment With Inside Information and Drift Uncertaintymentioning

confidence: 99%

“…Further examples of models with both inside information and parameter uncertainty can be found in Danilova, Monoyios and Ng [3].…”

Section: Introductionmentioning

confidence: 99%

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Optimal investment and hedging under partial and inside information

Albrecher¹,

Runggaldier²,

Schachermayer³

2009

Advanced Financial Modelling

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This article concerns optimal investment and hedging for agents who must use trading strategies which are adapted to the filtration generated by asset prices, possibly augmented with some inside information related to the future evolution of an asset price. The price evolution and observations are taken to be continuous, so the partial (and, when applicable, inside) information scenario is characterised by asset price processes with an unknown drift parameter, which is to be filtered from price observations. We first give an exposition of filtering theory, leading to the Kalman-Bucy filter. We outline the dual approach to portfolio optimisation, which is then applied to the Merton optimal investment problem when the agent does not know the drift parameter of the underlying stock. This is taken to be a random variable with a Gaussian prior distribution, which is updated via the Kalman filter. This results in a model with a stochastic drift process adapted to the observation filtration, and which can be treated as a full information problem, and an explicit solution to the optimal investment problem is possible. We also consider the same problem when the agent has noisy knowledge at time 0 of the terminal value of the Brownian motion driving the stock. Using techniques of enlargement of filtration to accommodate the insider's additional knowledge, followed by filtering the asset price drift, we are again able to obtain an explicit solution. Finally we treat an incomplete market hedging problem. A claim on a non-traded asset is hedged using a correlated traded asset. We summarise the full information case, then treat the partial information scenario in which the hedger is uncertain of the true values of the asset price drifts. After filtering, the resulting problem with random drifts is solved in the case that each asset's prior distribution has the same variance, resulting in analytic approximations for the optimal hedging strategy.

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“…This idea is extended to the case where expert opinions arrive continuously in time by Fouque, Papanicolaou and Sircar (2017) [16] and by Davis and Lleo (2013) [11] who implement the BlackâĂŞLitterman model in a continuous time setting and use separability of the filtering problem and the stochastic control problem to incorporate analyst views and non-tradeable assets as additional source of observation to estimate the filter. A similar setting has been studied by Danilova, Monoyios and Ng (2010) [10] who assumed that the investor has partial information about the drift of the stock price but also some privileged information about the future of stock price. In Putschögl and Sass (2008) [32] an optimal investment and consumption problem under partial observation is analysed using Malliavin calculus.…”

Section: Introductionmentioning

confidence: 98%

The Value of Knowing the Market Price of Risk

2019

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This paper presents an optimal allocation problem in a financial market with one risk-free and one risky asset, when the market is driven by a stochastic market price of risk. We solve the problem in continuous time, for an investor with a Constant Relative Risk Aversion (CRRA) utility, under two scenarios: when the market price of risk is observable (the full information case), and when it is not (the partial information case). The corresponding market models are complete in the partial information case and incomplete in the other case, hence the two scenarios exhibit rather different features. We study how the access to more accurate information on the market price of risk affects the optimal strategies and we determine the maximal price that the investor would be willing to pay to get such information. In particular, we examine two cases of additional information, when an exact observation of the market price of risk is available either at time 0 only (the initial information case), or during the whole investment period (the dynamic information case).

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Optimal investment with inside information and parameter uncertainty

Cited by 27 publications

References 32 publications

Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

Optimal investment and hedging under partial and inside information

The Value of Knowing the Market Price of Risk

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