Portfolio Optimization Under Partial Information With Expert Opinions

Frey, Rüdiger; Gabih, Abdelali; Wunderlich, Ralf

doi:10.1142/s0219024911006486

Cited by 53 publications

(50 citation statements)

References 14 publications

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“…Others consider the possibility that their agents' models have the correct form; however, the agents must gradually learn the values of certain unobserved features ( [17], [31], [43], [54], [62], [48]). …”

Section: Background and Contributionsmentioning

confidence: 99%

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Mini-Flash Crashes, Model Risk, and Optimal Execution

Bayraktar

Munk

2017

SSRN Journal

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Abstract. Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision, fundamental value shocks, and market fragmentation. We develop a mathematical model which captures aspects of the first three explanations. Empirical features of recent mini-flash crashes are present in our framework. For example, there are periods when no such events will occur. If they do, even just before their onset, market participants may not know with certainty that a disruption will unfold. Our mini-flash crashes can materialize in both low and high trading volume environments and may be accompanied by a partial synchronization in order submission.Instead of adopting a classically-inspired equilibrium approach, we borrow ideas from the optimal execution literature. Each of our agents begins with beliefs about how his own trades impact prices and how prices would move in his absence. They, along with other market participants, then submit orders which are executed at a common venue. Naturally, this leads us to explicitly distinguish between how prices actually evolve and our agents' opinions. In particular, every agent's beliefs will be expressly incorrect.As far as we know, this setup suggests both a new paradigm for modeling heterogeneous agent systems and a novel blueprint for understanding model misspecification risks in the context of optimal execution.

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Section: Background and Contributionsmentioning

confidence: 99%

“…A possible extension of our work could replace (4.2) with one of the more recent models considered in the literature on optimal trading problems with a learning aspect ( [17], [54], [43], [64], [86], [62], [48]). …”

Section: Preliminariesmentioning

confidence: 99%

Mini-Flash Crashes, Model Risk, and Optimal Execution

Bayraktar

Munk

2017

SSRN Journal

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“…Early works on partial information include Detemple (1986Detemple ( , 1991, who studies optimal technology investment problems (where the states that drive production are obfuscated by Gaussian noise); Gennotte (1986), who studies the optimal portfolio allocation problem when returns are hidden but satisfy an Ornstein-Uhlenbeck process; Dothan and Feldman (1986), who analyze a production and exchange economy with a single unobservable source of nondiversifiable risk; Karatzas and Xue (1991), who study utility maximization under partial observations; Bäuerle and Rieder (2005), Bäuerle and Rieder (2007), and Frey, Gabih, and Wunderlich (2012), who study model uncertainty in the context of portfolio optimization and the optimal allocation of assets; and Papanicolaou (2019), who studies an optimal portfolio allocation problem where the drift of the assets are latent Ito diffusions.…”

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confidence: 99%

Trading algorithms with learning in latent alpha models

Casgrain

Jaimungal

2018

Mathematical Finance

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Alpha signals for statistical arbitrage strategies are often driven by latent factors. This paper analyzes how to optimally trade with latent factors that cause prices to jump and diffuse. Moreover, we account for the effect of the trader's actions on quoted prices and the prices they receive from trading. Under fairly general assumptions, we demonstrate how the trader can learn the posterior distribution over the latent states, and explicitly solve the latent optimal trading problem. We provide a verification theorem, and a methodology for calibrating the model by deriving a variation of the expectation–maximization algorithm. To illustrate the efficacy of the optimal strategy, we demonstrate its performance through simulations and compare it to strategies that ignore learning in the latent factors. We also provide calibration results for a particular model using Intel Corporation stock as an example.

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“…At time t = 0, the expert opinions reveal the true value of Z 0 so that E Z 0 F 0 = Z 0 and var Z 0 F 0 = 0. We could generalize the framework to have expert opinions arriving at multiple stochastic times, as done in [FGW12], but this paper will consider the basic case where expert opinions come at time t = 0 only. Given the role and effects of expert opinions, we are ready to provide an interpretation of the multiple time scales in (Y t , Z t ): i).…”

Section: Model For Stochastic Returns and Filtering Equationsmentioning

confidence: 99%

Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions

2014

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Abstract. We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and then use this filter as input to a portfolio problem with an objective to maximize expected terminal utility. Our results apply for general concave utility functions. We incorporate time-scale separation in the fluctuations of the returns process, and utilize singular and regular perturbation analysis on the associated partial information HJB equation, which leads to an intuitive interpretation of the additional risk caused by uncertainty in expected returns. The results are an extension of the partially-informed investment strategies obtained by the Black-Litterman model, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.Key words. Filtering, control, Hamilton-Jacobi-Bellman equation, portfolio optimization, partial information, expert opinions. Subject classifications. 91G20, 60G35, 35Q93, 35C201. Introduction. It is well-known that optimal mean-variance portfolio weights are quite different from the weights used in real-life investment. As pointed out in [BL92], unconstrained optimization often results in large short positions among many asset classes, and constrained optimization results in zero weight in many assets and unreasonably large weights in assets with small capitalization. The model of Black and Litterman [BL91] is a practical solution to this problem, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.In continuous time or multi-period settings, a natural extension of the Black and Litterman model is to include a separate stochastic process for the level of expected returns. Due to the large amount of data required for accurate estimation of this new process, much of the existing literature considers it to be unobserved, hence making this an investment problem with only partial information. Several papers consider expected returns to be an unobserved Markov process and then use filtering methods (i.e. Kalman filter or Wonham filter) to track the hidden state. Indeed, investment with partial information is studied in [Bre98,Bre06,ESB10,BR05,FPS14,Pap13,Pha09,SH04]. The effect of this added stochasticity is that optimal investment strategies will change from those suggested by the standard Merton problem [Mer69], with the effects of riskaversion characteristics and the investment horizon playing a role in the solution [Bre98,Wac02].The analysis in [FGW12] combines filtering with so-called expert opinions, a concept which is similar to the Black-Litterman model's consideration of investors' views. The idea is the following: in a dynamic investment problem, the nature of...

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Portfolio Optimization Under Partial Information With Expert Opinions

Cited by 53 publications

References 14 publications

Mini-Flash Crashes, Model Risk, and Optimal Execution

Mini-Flash Crashes, Model Risk, and Optimal Execution

Trading algorithms with learning in latent alpha models

Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions

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