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 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.

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 Optimal portfolio policies under fixed and proportional transaction costs

2006 ◽  
Vol 38 (4) ◽  
pp. 916-942 ◽  
Author(s):  
Albrecht Irle ◽  
Jörn Sass
Keyword(s):  
Growth Rate ◽  
Impulse Control ◽  
Optimization Problem ◽  
One Dimension ◽  
Quasivariational Inequalities ◽  
Proportional Transaction Costs ◽  
Asymptotic Growth ◽  
Portfolio Optimization Problem ◽  
Asymptotic Growth Rate ◽  
Optimal Impulse

We consider the portfolio optimization problem of maximizing the asymptotic growth rate under a combination of fixed and proportional costs. Expressing the asymptotic growth rate in terms of the risky fraction process, the problem can be transformed to that of controlling a diffusion in one dimension. Then we use the corresponding quasivariational inequalities to obtain the explicit shape together with the existence of an optimal impulse control strategy. This optimal strategy is given by only four parameters: two for the stopping boundaries and two for the new risky fractions the investor chooses at these times.

scholarly journals Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters

2021 ◽  
Vol 26 (2) ◽  
pp. 36
Author(s):  
Alejandro Estrada-Padilla ◽  
Daniela Lopez-Garcia ◽  
Claudia Gómez-Santillán ◽  
Héctor Joaquín Fraire-Huacuja ◽  
Laura Cruz-Reyes ◽  
...  
Keyword(s):  
Steady State ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Solution Process ◽  
Density Estimator ◽  
Nsga Ii ◽  
Spatial Spread ◽  
Multi Objective ◽  
Significant Difference ◽  
Portfolio Optimization Problem

A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology.

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