Trading algorithms with learning in latent alpha models

Casgrain, Philippe; Jaimungal, Sebastian

doi:10.1111/mafi.12194

Cited by 34 publications

(31 citation statements)

References 33 publications

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“…In this part, we provide an example model where the asset price process is modulated by a latent Markov chain similarly to that in Casgrain and Jaimungal (). In our model, we assume each subpopulation disagrees on the distribution of initial value of the latent process, while they do agree on what the possible values of the latent state are, and agree on the transition rates between states.…”

Section: An Example Model Of Disagreementmentioning

confidence: 99%

“…In contrast to other work on MFGs, as well as its specific application to algorithmic trading, here, motivated by Casgrain and Jaimungal (), we include latent states, so that agents do not have full information about the system dynamics. Furthermore, motivated by Firoozi and Caines () and Casgrain and Jaimungal (), who study a stochastic game with latent factors where agents have the same model beliefs, here, we study how varying beliefs among the agents affect the optimal trading behavior.…”

Section: Introductionmentioning

confidence: 99%

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Mean‐field games with differing beliefs for algorithmic trading

Casgrain

Jaimungal

2020

Mathematical Finance

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Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for the permanent impact they have on prices. This leads to a large stochastic game, where each agents' performance criteria is computed under a different probability measure. We analyse the mean-field game (MFG) limit of the stochastic game and show that the Nash equilibria is given by the solution to a non-standard vector-valued forward-backward stochastic differential equation. Under some mild assumptions, we construct the solution in terms of expectations of the filtered states. We prove the MFG strategy forms an -Nash equilibrium for the finite player game.Lastly, we present a least-squares Monte Carlo based algorithm for computing the optimal control and illustrate the results through simulation in market where agents disagree on the model. 1. Introduction. Financial markets are immensely complicated dynamic systems which incorporate the interactions of millions of individuals on a daily basis. Market participants vary immensely, both in terms of their trading objectives and in their beliefs on the assets they are trading. All of these participants compete with one another in an attempt to achieve their own personal objectives in the most efficient way possible. Traded assets may also be driven by latent factors, and agents must dynamically incorporate data into their trading decisions.In this paper, we propose a game theoretic model in which a large population of heterogeneous agents all trade the same asset. This model considers heterogeneity not only from the point of view of an individual's trading objectives and risk appetite, but also from the point of view of each agent's beliefs regarding the performance of the asset they are trading. We pay particular attention to the information each agent is privy to, in an attempt to render the framework as realistic as possible, while maintaining some semblance of tractability.We study the equilibrium of these markets by using the theory of mean-field games (MFGs), which serves to describe Game-Theoretic models as the number of participating agents becomes extremely large. The general theory of mean-field games already has a large * SJ would like to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference numbers RGPIN-2018-05705 and RGPAS-2018-522715]

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Section: An Example Model Of Disagreementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mean‐field games with differing beliefs for algorithmic trading

Casgrain

Jaimungal

2020

Mathematical Finance

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“…Since then, market impact models have been extensively studied. Important contributions include He and Mamaysky [30], Schied and Schöneborn [35], Schied [34], Guo and Zervos [29], Casgrain and Jaimungal [14]. All these models work in a (discretized) diffusion framework.…”

Section: Introductionmentioning

confidence: 99%

Optimal liquidation under partial information with price impact

Colaneri

Eksi

Frey

et al. 2020

Stochastic Processes and their Applications

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We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finite-state Markov chain and by the liquidation rate. This model is consistent with stylized facts of high frequency data such as the discrete nature of tick data and the clustering in the order flow. We include both temporary and permanent effects into our analysis. We use stochastic filtering to reduce the optimal liquidation problem to an equivalent optimization problem under complete information. This leads to a stochastic control problem for piecewise deterministic Markov processes (PDMPs). We carry out a detailed mathematical analysis of this problem. In particular, we derive the optimality equation for the value function, we characterize the value function as continuous viscosity solution of the associated dynamic programming equation, and we prove a novel comparison result. The paper concludes with numerical results illustrating the impact of partial information and price impact on the value function and on the optimal liquidation rate.

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“…Bäuerle and Rieder (2007) introduces jumps to the asset price dynamics by including Poisson random measures with unobservable intensity processes. Latent models are also central to the work of Casgrain and Jaimungal (2018b) and Casgrain and Jaimungal (2018a) in the context of algorithmic trading and mean field games.…”

Section: Introductionmentioning

confidence: 99%

Active and Passive Portfolio Management with Latent Factors

Al-Aradi

Jaimungal

2019

SSRN Journal

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We address a portfolio selection problem that combines active (outperformance) and passive (tracking) objectives using techniques from convex analysis. We assume a general semimartingale market model where the assets' growth rate processes are driven by a latent factor. Using techniques from convex analysis we obtain a closed-form solution for the optimal portfolio and provide a theorem establishing its uniqueness. The motivation for incorporating latent factors is to achieve improved growth rate estimation, an otherwise notoriously difficult task. To this end, we focus on a model where growth rates are driven by an unobservable Markov chain. The solution in this case requires a filtering step to obtain posterior probabilities for the state of the Markov chain from asset price information, which are subsequently used to find the optimal allocation. We show the optimal strategy is the posterior average of the optimal strategies the investor would have held in each state assuming the Markov chain remains in that state. Finally, we implement a number of historical backtests to demonstrate the performance of the optimal portfolio.

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Trading algorithms with learning in latent alpha models

Cited by 34 publications

References 33 publications

Mean‐field games with differing beliefs for algorithmic trading

Mean‐field games with differing beliefs for algorithmic trading

Optimal liquidation under partial information with price impact

Active and Passive Portfolio Management with Latent Factors

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