Optimal Control Under Uncertainty and Bayesian Parameters Adjustments

@article{Baradel2016OptimalCU,
  title={Optimal Control Under Uncertainty and Bayesian Parameters Adjustments},
  author={Nicolas Baradel and Bruno Bouchard and Ngoc-Minh Dang},
  journal={SIAM J. Control. Optim.},
  year={2016},
  volume={56},
  pages={1038-1057}
}
We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the classical Bayesian rule after each impulse. Taking these progressive prior-adjustments into account, we characterize the optimal policy through a quasi-variational parabolic equation, which can be solved numerically. The derivation of the dynamic programming… 

Optimal control under uncertainty: Application to the issue of CAT bonds

We propose a general framework for studying optimal issue of CAT bonds in the presence of uncertainty on the parameters. In particular, the intensity of arrival of natural disasters is inhomogeneous

Optimal Trading with Online Parameter Revisions

It is explained how a mix of the classical Bayesian updating rule and of optimal control techniques allows one to derive the dynamic programming equation satisfied by the corresponding value function, from which the optimal policy can be inferred.

Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a

Optimal inventory management and order book modeling

This work derives the variational partial differential equations that characterize the value functions of the MM, high-frequency trading firms, and institutional brokers and explains how almost optimal control can be deduced from them.

A hybrid stochastic river environmental restoration modeling with discrete and costly observations

A recent river environmental restoration problem is approached from a standpoint of stochastic control of hybrid regime‐switching diffusion processes with discrete and costly observations. This

Contrôle optimal, apprentissage statistique et modélisation du carnet d'ordres

L'objectif principal de cette these est de comprendre les interactions entre les agents financiers et le carnet d'ordres. Elle se compose de six chapitres inter-connectes qui peuvent toutefois etre

References

SHOWING 1-10 OF 26 REFERENCES

Optimal Trading with Online Parameter Revisions

It is explained how a mix of the classical Bayesian updating rule and of optimal control techniques allows one to derive the dynamic programming equation satisfied by the corresponding value function, from which the optimal policy can be inferred.

Controlling a Stochastic Process with Unknown Parameters

The problem of controlling a stochastic process, with unknown parameters over an infinite horizon, with discounting is considered. Agents express beliefs about unknown parameters in terms of

A stochastic target formulation for optimal switching problems in finite horizon

We consider a general optimal switching problem for a controlled diffusion and show that its value coincides with the value of a well-suited stochastic target problem associated to a diffusion with

A Finite Element Like Scheme for Integro-Partial Differential Hamilton-Jacobi-Bellman Equations

A finite element like scheme for fully nonlinear integro-partial differential equations arising in optimal control of jump-processes is constructed and it is proved that they converge in very general situations, including degenerate equations, multiple dimensions, relatively low regularity of the data, and for most (if not all) types ofJump-models used in finance.

Weak Dynamic Programming Principle for Viscosity Solutions

We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the

An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications

In this course, we first present an elementary introduction to the concept of viscosity solutions for first-order Hamilton–Jacobi Equations: definition, stability and comparison results (in the

Optimal dealer pricing under transactions and return uncertainty

Dealing with the inventory risk: a solution to the market making problem

Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they

Stochastic optimal control : the discrete time case

This research monograph is the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including the treatment of the

Optimal Portfolio Liquidation with Limit Orders

The interactions of limit orders with the market are modeled via a Poisson process pegged to a diffusive "fair price" and a Hamilton-Jacobi-Bellman equation is used to solve the problem involving both non-execution risk and price risk.