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 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.

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.

Growth in Baumslag–Solitar groups II: The Bass–Serre tree

2020 ◽  
Vol 30 (02) ◽  
pp. 339-378
Author(s):  
Jared Adams ◽  
Eric M. Freden
Keyword(s):  
Growth Rate ◽  
Minimal Length ◽  
Geometric Object ◽  
Asymptotic Growth ◽  
Growth Series ◽  
Context Sensitive ◽  
Counting Algorithms ◽  
Self Similar ◽  
Context Free ◽  
Asymptotic Growth Rate

Denote the Baumslag–Solitar family of groups as [Formula: see text]). When [Formula: see text] we study the Bass–Serre tree [Formula: see text] for [Formula: see text] as a geometric object. We suggest that the irregularity of [Formula: see text] is the principal obstruction for computing the growth series for the group. In the particular case [Formula: see text] we exhibit a set [Formula: see text] of normal form words having minimal length for [Formula: see text] and use it to derive various counting algorithms. The language [Formula: see text] is context-sensitive but not context-free. The tree [Formula: see text] has a self-similar structure and contains infinitely many cone types. All cones have the same asymptotic growth rate as [Formula: see text] itself. We derive bounds for this growth rate, the lower bound also being a bound on the growth rate of [Formula: see text].

Bisexual Galton–Watson branching processes with superadditive mating functions

1986 ◽  
Vol 23 (03) ◽  
pp. 585-600 ◽  
Author(s):  
D. J. Daley ◽  
David M. Hull ◽  
James M. Taylor
Keyword(s):  
Growth Rate ◽  
Branching Process ◽  
Critical Case ◽  
Branching Processes ◽  
Upper And Lower Bounds ◽  
Simple Criterion ◽  
Asymptotic Growth ◽  
Extinction Probabilities ◽  
Mating Function ◽  
Asymptotic Growth Rate

For a bisexual Galton–Watson branching process with superadditive mating function there is a simple criterion for determining whether or not the process becomes extinct with probability 1, namely, that the asymptotic growth rate r should not exceed 1. When extinction is not certain (equivalently, r > 1), simple upper and lower bounds are established for the extinction probabilities. An example suggests that in the critical case that r = 1, some condition like superadditivity is essential for ultimate extinction to be certain. Some illustrative numerical comparisons of particular mating functions are made using a Poisson offspring distribution.

scholarly journals Bounds for the Asymptotic Growth Rate of an Age-Dependent Branching Process

1969 ◽  
Vol 10 (1-2) ◽  
pp. 231-235 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Growth Rate ◽  
Population Size ◽  
Branching Process ◽  
Expected Number ◽  
Lattice Distribution ◽  
Asymptotic Growth ◽  
Age Dependent ◽  
The Mean ◽  
Image Position ◽  
Asymptotic Growth Rate

Let M(t) denote the mean population size at time t (conditional on a single ancestor of age zero at time zero) of a branching process in which the distribution of the lifetime T of an individual is given by Pr {T≦t} =G(t), and in which each individual gives rise (at death) to an expected number A of offspring (1λ A λ ∞). expected number A of offspring (1 < A ∞). Then it is well-known (Harris [1], p. 143) that, provided G(O+)-G(O-) 0 and G is not a lattice distribution, M(t) is given asymptotically by where c is the unique positive value of p satisfying the equation .

Bisexual Galton–Watson branching processes with superadditive mating functions

1986 ◽  
Vol 23 (3) ◽  
pp. 585-600 ◽  
Author(s):  
D. J. Daley ◽  
David M. Hull ◽  
James M. Taylor
Keyword(s):  
Growth Rate ◽  
Branching Process ◽  
Critical Case ◽  
Branching Processes ◽  
Upper And Lower Bounds ◽  
Simple Criterion ◽  
Asymptotic Growth ◽  
Extinction Probabilities ◽  
Mating Function ◽  
Asymptotic Growth Rate

For a bisexual Galton–Watson branching process with superadditive mating function there is a simple criterion for determining whether or not the process becomes extinct with probability 1, namely, that the asymptotic growth rate r should not exceed 1. When extinction is not certain (equivalently, r > 1), simple upper and lower bounds are established for the extinction probabilities. An example suggests that in the critical case that r = 1, some condition like superadditivity is essential for ultimate extinction to be certain. Some illustrative numerical comparisons of particular mating functions are made using a Poisson offspring distribution.

scholarly journals Some Local Asymptotic Laws for the Cauchy Process on the Line

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
A. Chukwuemeka Okoroafor
Keyword(s):  
Growth Rate ◽  
Sojourn Time ◽  
Escape Rate ◽  
Time Process ◽  
Rate Process ◽  
Monotone Functions ◽  
Asymptotic Growth ◽  
Asymptotic Size ◽  
Asymptotic Growth Rate ◽  
Cauchy Process

This paper investigates the lim inf behavior of the sojourn time process and the escape rate process associated with the Cauchy process on the line. The monotone functions associated with the lower asymptotic growth rate of the sojourn time are characterized and the asymptotic size of the large values of the escape rate process is developed.

On the asymptotic growth rate of some spanning trees embedded in

2011 ◽  
Vol 39 (1) ◽  
pp. 44-48 ◽  
Author(s):  
Pedro M.M. de Castro ◽  
Olivier Devillers
Keyword(s):  
Growth Rate ◽  
Spanning Trees ◽  
Asymptotic Growth ◽  
Asymptotic Growth Rate
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