scholarly journals Growth-Optimal Strategies with Quadratic Friction over Finite-Time Investment Horizons

2003 ◽  
Author(s):  
Erik M. Aurell ◽  
Paolo Muratore-Ginanneschi
Keyword(s):  
Finite Time ◽  
Optimal Strategies ◽  
Time Investment

scholarly journals GROWTH-OPTIMAL STRATEGIES WITH QUADRATIC FRICTION OVER FINITE-TIME INVESTMENT HORIZONS

2004 ◽  
Vol 07 (05) ◽  
pp. 645-657 ◽  
Author(s):  
ERIK AURELL ◽  
PAOLO MURATORE-GINANNESCHI
Keyword(s):  
Transaction Costs ◽  
Finite Time ◽  
Optimal Strategy ◽  
Time Horizon ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Market Model ◽  
Time Investment ◽  
Bond Portfolio ◽  
Finite Time Horizon

We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. The size of the holding interval is determined by the intensity of the transaction costs and the time horizon.

Some risk management problems for firms with internal competition and debt

2002 ◽  
Vol 39 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Xin Guo
Keyword(s):  
Finite Time ◽  
Singular Control ◽  
Optimal Strategies ◽  
Control Policy ◽  
Optimal Investment ◽  
Optimal Size ◽  
Business Practices ◽  
Business Unit ◽  
Average Return ◽  
Internal Competition

Consider an optimization problem for a company with the following parameters: a constant liability payment rate (δ), an average return (μ) and a risk (σ) proportional to the size of the business unit, and an internal competition factor (α) between different units. The goal is to maximize the expected present value of the total dividend distributions, via controls (Ut, Zt), where Ut is the size of the business unit and Zt is the total dividend payoff up to time t. We formulate this as a stochastic control problem for a diffusion process Xt and derive an explicit solution by solving the corresponding Hamilton-Jacobi-Bellman equation. The resulting optimal control policy involves a mixture of a nonlinear control for Ut and a singular control for Zt. The optimal strategies are different for the cases δ < 0 and δ = 0. When δ > 0, it is optimal to play bold: the initial optimal investment size should be proportional to the debt rate δ. Under this optimal rule, however, the probability of bankruptcy in finite time is 1. When δ = 0, i.e. when the company is free of debt, the probability of going broke in finite time reduces to 0. Moreover, when δ = 0, the value function is singular at X0 = 0. Our analytical result shows considerable consistency with daily business practices. For instance, it shows that ‘too many people is counter-productive’. In fact, the maximal optimal size of the business unit should be inversely proportional to α. This eliminates the redundant and simplistic technical assumption of a known uniform upper bound on the size of the firm.

Some risk management problems for firms with internal competition and debt

2002 ◽  
Vol 39 (01) ◽  
pp. 55-69 ◽  
Author(s):  
Xin Guo
Keyword(s):  
Finite Time ◽  
Singular Control ◽  
Optimal Strategies ◽  
Control Policy ◽  
Optimal Investment ◽  
Optimal Size ◽  
Business Practices ◽  
Business Unit ◽  
Average Return ◽  
Internal Competition

Consider an optimization problem for a company with the following parameters: a constant liability payment rate (δ), an average return (μ) and a risk (σ) proportional to the size of the business unit, and an internal competition factor (α) between different units. The goal is to maximize the expected present value of the total dividend distributions, via controls (U t , Z t ), where U t is the size of the business unit and Z t is the total dividend payoff up to time t. We formulate this as a stochastic control problem for a diffusion process X t and derive an explicit solution by solving the corresponding Hamilton-Jacobi-Bellman equation. The resulting optimal control policy involves a mixture of a nonlinear control for U t and a singular control for Z t . The optimal strategies are different for the cases δ &lt; 0 and δ = 0. When δ &gt; 0, it is optimal to play bold: the initial optimal investment size should be proportional to the debt rate δ. Under this optimal rule, however, the probability of bankruptcy in finite time is 1. When δ = 0, i.e. when the company is free of debt, the probability of going broke in finite time reduces to 0. Moreover, when δ = 0, the value function is singular at X 0 = 0. Our analytical result shows considerable consistency with daily business practices. For instance, it shows that ‘too many people is counter-productive’. In fact, the maximal optimal size of the business unit should be inversely proportional to α. This eliminates the redundant and simplistic technical assumption of a known uniform upper bound on the size of the firm.

Rubber Composition–Properties Relationships during Tire Numerical Simulation and Design Optimization

2017 ◽  
Vol 45 (1) ◽  
pp. 71-84 ◽  
Author(s):  
Alexey Mazin ◽  
Alexander Kapustin ◽  
Mikhail Soloviev ◽  
Alexander Karanets
Keyword(s):  
Numerical Simulation ◽  
Design Optimization ◽  
Strain Tensor ◽  
General Purpose ◽  
Orthogonal Functions ◽  
Element Analysis ◽  
Time Investment ◽  
Footprint Analysis ◽  
Composition Properties ◽  
Nonlinear Elastic

ABSTRACT Numerical simulation based on finite element analysis is now widely used during the design optimization of tires, thereby drastically reducing the time investment in the design process and improving tire performance because it is obtained from the optimized solution. Rubber material models that are used in numerical calculations of stress–strain distributions are nonlinear and may include several parameters. The relations of these parameters with rubber formulations are usually unknown, so the designer has no information on whether the optimal set of parameters is reachable by the rubber technological possibilities. The aim of this work was to develop such relations. The most common approach to derive the equation of the state of rubber is based on the expansion of the strain energy in a series of invariants of the strain tensor. Here, we show that this approach has several drawbacks, one of which is problems that arise when trying to build on its basis the quantitative relations between the rubber composition and its properties. An alternative is to use a series expansion in orthogonal functions, thereby ensuring the linear independence of the coefficients of elasticity in evaluation of the experimental data and the possibility of constructing continuous maps of “the composition to the property.” In the case of orthogonal Legendre polynomials, the technique for constructing such maps is considered, and a set of empirical functions is proposed to adequately describe the dependence of the parameters of nonlinear elastic properties of general-purpose rubbers on the content of the main ingredients. The calculated sets of parameters were used in numerical tire simulations including static loading, footprint analysis, braking/acceleration, and cornering and also in design optimization procedures.

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