Backward SDEs for Control with Partial Information

Papanicolaou, Andrew C.

doi:10.2139/ssrn.2569529

Cited by 4 publications

(11 citation statements)

References 3 publications

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“…Early works on partial information include Detemple (1986), Detemple (1991), who study 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 analyzes a production and exchange economy with a single unobservable source of nondiversifiable risk; Karatzas and Xue (1991), who studies utility maximization under partial observations; Bäuerle and Rieder (2005), Bäuerle and Rieder (2007) and Frey et al (2012), who study model uncertainty in the context of portfolio optimization and the optimal allocation of assets; and Papanicolaou (2018), who studies an optimal portfolio allocation problem where the drift of the assets are latent Ito diffusions.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Trading algorithms with learning in latent alpha models

Casgrain

Jaimungal

2018

Mathematical Finance

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“…They are Kalman-Bucy filter for linear diffusion, Wonham filter for finite state Markov chain, and Bayesian filter for random variable. Each of them has been widely studied in portfolio optimization, see, for example, Lakner [15] and Papanicolaou [18] for the linear diffusion model, Sass and Haussmann [21] and Eksi and Ku [7] for the continuous-time finite state Markov chain model, Ekstrom and Vaicenavicius [8] and Bismuth et al [3] for the random variable model. All the aforementioned papers deal with only specific (power or logarithmic) utility without control constraints.…”

Section: Introductionmentioning

confidence: 99%

Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty

Zhu

Zheng

2022

J Optim Theory Appl

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In this paper, we propose a novel and effective approximation method for finding the value function for general utility maximization with closed convex control constraints and partial information. Using the separation principle and the weak duality relation, we transform the stochastic maximum principle of the fully observable dual control problem into an equivalent error minimization stochastic control problem and find the tight lower and upper bounds of the value function and its approximate value. Numerical examples show the goodness and usefulness of the proposed method.

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“…Classicial works include [42], [27], and [12], among others. Duality approach was developed in [29] and [45] and has become a useful tool to solve incomplete market model, with [39] a recent application with partial information. Problems with portfolio constraints was in [13] and [51], among others.…”

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confidence: 99%

“…In addition to the Merton proportion, the strategy includes a hedging demand for the volatility of the return process. [39] used results from filtering, duality, and the BSDE theory to solve the investment problem, which includes the case of an unbounded mean return. It argues that the BSDE solution is the unique limit of solutions to a sequence of truncated problems with unique solutions obtained by a martingale representation theorem.…”

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confidence: 99%

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Relative wealth concerns with partial information and heterogeneous priors

Deng¹,

Su²,

Zhou³

2020

Preprint

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We establish a Nash equilibrium in a market with N agents with the performance criteria of relative wealth level when the market return is unobservable. Each investor has a random prior belief on the return rate of the risky asset. The investors can be heterogeneous in both the mean and variance of the prior. By a separation result and a martingale argument, we show that the optimal investment strategy under a stochastic return rate model can be characterized by a fully-coupled linear FBSDE. Two sets of deep neural networks are used for the numerical computation to first find each investor's estimate of the mean return rate and then solve the FBSDEs. We establish the existence and uniqueness result for the class of FBSDEs with stochastic coefficients and solve the utility game under partial information using deep neural network function approximators. We demonstrate the efficiency and accuracy by a base-case comparison with the solution from the finite difference scheme in the linear case and apply the algorithm to the general case of nonlinear hidden variable process. Simulations of investment strategies show a herd effect that investors trade more aggressively under relativeness concerns. Statistical properties of the investment strategies and the portfolio performance, including the Sharpe ratios and the Variance Risk ratios (VRRs) are examed. We observe that the agent with the most accurate prior estimate is likely to lead the herd, and the effect of competition on heterogeneous agents varies more with market characteristics compared to the homogeneous case.

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Backward SDEs for Control with Partial Information

Cited by 4 publications

References 3 publications

Trading algorithms with learning in latent alpha models

Trading algorithms with learning in latent alpha models

Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty

Relative wealth concerns with partial information and heterogeneous priors

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