scholarly journals Optimal Trading with Online Parameter Revisions

2016 ◽  
Vol 02 (03n04) ◽  
pp. 1750003
Author(s):  
N. Baradel ◽  
B. Bouchard ◽  
N. M. Dang
Keyword(s):  
Optimal Control ◽  
Impulse Control ◽  
Value Function ◽  
Unknown Parameters ◽  
Control Techniques ◽  
Optimal Trading ◽  
Impulse Control Problem ◽  
Dynamic Programming Equation ◽  
Market Impacts ◽  
Optimal Impulse

The aim of this paper is to explain how parameters adjustments can be integrated in the design or the control of automates of trading. Typically, we are interested in the online estimation of the market impacts generated by robots or single orders, and how they/the controller should react in an optimal way to the information generated by the observation of the realized impacts. This can be formulated as an optimal impulse control problem with unknown parameters, on which a prior is given. We explain 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. We provide an example of convergent finite difference scheme and consider typical examples of applications.

A Class of Stochastic Control Problem Governed by a Poisson Process

2012 ◽  
Vol 450-451 ◽  
pp. 46-55
Author(s):  
Shao Lin Tian ◽  
Ji Chun Li ◽  
Kun Hui Liu
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Poisson Process ◽  
Objective Function ◽  
Impulse Control ◽  
Sufficient Condition ◽  
Signal Process ◽  
Impulse Control Problem ◽  
State Process ◽  
Optimal Impulse

In this paper, we examine an optimal impulse control problem of stochastic system, whose state follows a Brownian motion. Here we want to maximum the objective function. The main feature of our model is that the controlled state process includes an impulse control governed by a Poisson process. In other words, the set of possible intervention times are discrete, random and determined by the signal process. Here we not only present a theorem giving a sufficient condition on the existence of an optimal control and its corresponding objective function, but also provide an explicit solution obtained under some simplified conditions.

OPTIMAL DIVIDEND–REINSURANCE WITH TWO TYPES OF PREMIUM PRINCIPLES

2015 ◽  
Vol 30 (2) ◽  
pp. 224-243 ◽  
Author(s):  
Hui Meng ◽  
Ming Zhou ◽  
Tak Kuen Siu
Keyword(s):  
Numerical Analysis ◽  
Impulse Control ◽  
Value Function ◽  
Proportional Transaction Costs ◽  
Ruin Time ◽  
Closed Form Solutions ◽  
Impulse Control Problem ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
The Value Function

A combined optimal dividend/reinsurance problem with two types of insurance claims, namely the expected premium principle and the variance premium principle, is discussed. Dividend payments are considered with both fixed and proportional transaction costs. The objective of an insurer is to determine an optimal dividend–reinsurance policy so as to maximize the expected total value of discounted dividend payments to shareholders up to ruin time. The problem is formulated as an optimal regular-impulse control problem. Closed-form solutions for the value function and optimal dividend–reinsurance strategy are obtained in some particular cases. Finally, some numerical analysis is given to illustrate the effects of safety loading on optimal reinsurance strategy.

scholarly journals Hereditary Portfolio Optimization with Taxes and Fixed Plus Proportional Transaction Costs—Part I

2007 ◽  
Vol 2007 ◽  
pp. 1-33 ◽  
Author(s):  
Mou-Hsiung Chang
Keyword(s):  
Portfolio Optimization ◽  
Impulse Control ◽  
Optimization Problem ◽  
Value Function ◽  
Infinite Time ◽  
Proportional Transaction Costs ◽  
Infinite Dimensional ◽  
Impulse Control Problem ◽  
Portfolio Optimization Problem ◽  
The Value Function

This is the first of the two companion papers which treat an infinite time horizon hereditary portfolio optimization problem in a market that consists of one savings account and one stock account. Within the solvency region, the investor is allowed to consume from the savings account and can make transactions between the two assets subject to paying capital gain taxes as well as a fixed plus proportional transaction cost. The investor is to seek an optimal consumption-trading strategy in order to maximize the expected utility from the total discounted consumption. The portfolio optimization problem is formulated as an infinite dimensional stochastic classical-impulse control problem. The quasi-variational HJB inequality (QVHJBI) for the value function is derived in this paper. The second paper contains the verification theorem for the optimal strategy. It is also shown there that the value function is a viscosity solution of the QVHJBI.

scholarly journals Continuity of the value function for deterministic optimal impulse control with terminal state constraint

2021 ◽  
Author(s):  
Yue Zhou ◽  
Xinwei Feng ◽  
Jiongmin Yong
Keyword(s):  
Viscosity Solution ◽  
Impulse Control ◽  
Value Function ◽  
State Constraint ◽  
Terminal State ◽  
Dynamic Programming Principle ◽  
Hamilton Jacobi Bellman ◽  
Optimal Impulse ◽  
The Value Function ◽  
Terminal State Constraint

Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is the introduction of an intrinsic condition under which the value function is proved to be continuous. Then by a Bellman dynamic programming principle, the corresponding Hamilton-Jacobi-Bellman type quasi-variational inequality (QVI, for short) is derived. The value function is proved to be a viscosity solution to such a QVI. The issue of whether the value function is characterized as the unique viscosity solution to this QVI is carefully addressed and the answer is left open challengingly.

A comparison of active vibration control techniques - Output feedback vs optimal control

1987 ◽  
Author(s):  
ZORAN MARTINOVIC ◽  
RAPHAEL HAFTKA ◽  
WILLIAM HALLAUER, JR. ◽  
GEORGE SCHAMEL, II
Keyword(s):  
Optimal Control ◽  
Vibration Control ◽  
Output Feedback ◽  
Active Vibration Control ◽  
Control Techniques ◽  
Active Vibration
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