Sliding modes in infinite-dimensional dynamic systems with impulse control

2002 ◽  
Author(s):  
M.V. Basin
Keyword(s):  
Dynamic Systems ◽  
Impulse Control ◽  
Sliding Modes ◽  
Infinite Dimensional

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

2007 ◽  
Vol 2007 ◽  
pp. 1-25 ◽  
Author(s):  
Mou-Hsiung Chang
Keyword(s):  
Transaction Costs ◽  
Portfolio Optimization ◽  
Impulse Control ◽  
Stock Price ◽  
Optimization Problem ◽  
Proportional Transaction Costs ◽  
Infinite Dimensional ◽  
Hereditary Nature ◽  
Portfolio Optimization Problem ◽  
The Value Function

This paper is the continuation of the paper entitled “Hereditary portfolio optimization with taxes and fixed plus proportional transaction costs I” that treats 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 due to the hereditary nature of the stock price dynamics and inventories. This paper contains the verification theorem for the optimal strategy. It also proves that the value function is a viscosity solution of the QVHJBI.

Attainability Sets of Dynamic Systems with Impulse Control

2000 ◽  
Vol 33 (16) ◽  
pp. 629-633
Author(s):  
V.V. Revenko ◽  
A.N. Sesekin ◽  
A.V. Stephanova
Keyword(s):  
Dynamic Systems ◽  
Impulse Control

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.

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