Dynamic Portfolio Selection

2017 ◽  
pp. 116-140
Keyword(s):  
Portfolio Optimization ◽  
Asset Allocation ◽  
Piecewise Linear ◽  
Relevant Literature ◽  
Asset Price ◽  
Piecewise Linear Function ◽  
Simple Formulation ◽  
Wolfram Mathematica ◽  
Dynamic Portfolio ◽  
Algorithmic Construction

In this chapter I recognize the importance of the stochastic programming as a significant tool in financial planning. The current practice of portfolio optimization is still limited to the simple formulation of linear programming (LR) or quadratic programming (QR) type. For that reason, relevant literature on asset-liability management (ALM) model has been reviewed and two different ALM approaches are compared: first piecewise linear function; and second a nonlinear utility function. This chapter shows that the mathematical programming methodology is ready to challenge the huge problem arising from LP portfolio optimization. A special emphasis was put on the shape of the investors' payoff functions in asset price equilibrium. The results underpin our claim that the nonlinear ALM model generated better asset allocation. An algorithmic construction of ALM model is developed in Wolfram Mathematica 9.

Dynamic portfolio selection with nonlinear transaction costs

2005 ◽  
Vol 461 (2062) ◽  
pp. 3183-3212 ◽  
Author(s):  
Thamayanthi Chellathurai ◽  
Thangaraj Draviam
Keyword(s):  
Transaction Costs ◽  
Portfolio Selection ◽  
Piecewise Linear ◽  
Singular Control ◽  
Econ Theory ◽  
Piecewise Linear Function ◽  
Risky Asset ◽  
Necessary Condition ◽  
Discounted Utility ◽  
Dynamic Portfolio

The dynamic portfolio selection problem with bankruptcy and nonlinear transaction costs is studied. The portfolio consists of a risk-free asset, and a risky asset whose price dynamics is governed by geometric Brownian motion. The investor pays transaction costs as a (piecewise linear) function of the traded volume of the risky asset. The objective is to find the stochastic controls (amounts invested in the risky and risk-free assets) that maximize the expected value of the discounted utility of terminal wealth. The problem is formulated as a non-singular stochastic optimal control problem in the sense that the necessary condition for optimality leads to explicit relations between the controls and the value function. The formulation follows along the lines of Merton (Merton 1969 Rev. Econ. Stat. 51 , 247–257; Merton 1971 J. Econ. Theory 3 , 373–413) and Bensoussan & Julien (Bensoussan & Julien 2000 Math. Finance 10 , 89–108) in the sense that the controls are the amounts of the risky asset bought and sold, and they are bounded. It differs from the works of Davis & Norman (Davis & Norman 1990 Math. Oper. Res. 15 , 676–713), who use, in the presence of proportional transaction costs, a singular-control formulation in which the controls are rates of buying and selling of the risky asset, and they are unbounded. Numerical results are presented for buy/no transaction and sell/no transaction interfaces, which characterize the optimal policies of a constant relative risk aversion investor. The no transaction region, in the presence of nonlinear transaction costs, is not a cone. The Merton line, on which no transaction takes place in the limiting case of zero transaction costs, need not lie inside the no transaction region for all values of wealth.

STOCHASTIC MODEL PREDICTIVE CONTROL AND PORTFOLIO OPTIMIZATION

2007 ◽  
Vol 10 (02) ◽  
pp. 203-233 ◽  
Author(s):  
FLORIAN HERZOG ◽  
GABRIEL DONDI ◽  
HANS P. GEERING
Keyword(s):  
Optimal Control ◽  
Portfolio Optimization ◽  
Predictive Control ◽  
Asset Allocation ◽  
Optimization Problem ◽  
Open Loop ◽  
Dynamic Portfolio ◽  
Portfolio Optimization Problem ◽  
Dynamic Portfolio Optimization

This paper proposes a solution method for the discrete-time long-term dynamic portfolio optimization problem with state and asset allocation constraints. We use the ideas of Model Predictive Control (MPC) to solve the constrained stochastic control problem. MPC is a solution technique which was developed to solve constrained optimal control problems for deterministic control applications. MPC solves the optimal control problem with a receding horizon where a series of consecutive open-loop optimal control problems is solved. The aim of this paper is to develop an MPC approach to the problem of long-term portfolio optimization when the expected returns of the risky assets are modeled using a factor model based on stochastic Gaussian processes. We prove that MPC is a suboptimal control strategy for stochastic systems which uses the new information advantageously and thus is better than the pure optimal open-loop control. For the open-loop optimal control optimization, we derive the conditional portfolio distribution and the corresponding conditional portfolio mean and variance. The mean and the variance depend on future decision about the asset allocation. For the dynamic portfolio optimization problem, we consider constraints on the asset allocation as well as probabilistic constraints on the attainable values of the portfolio wealth. We discuss two different objectives, a classical mean–variance objective and the objective to maximize the probability of exceeding a predetermined value of the portfolio. The dynamic portfolio optimization problem is stated, and the solution via MPC is explained in detail. The results are then illustrated in a case study.

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

scholarly journals Portfolio Optimization Constrained by Performance Attribution

2021 ◽  
Vol 14 (5) ◽  
pp. 201
Author(s):  
Yuan Hu ◽  
W. Brent Lindquist ◽  
Svetlozar T. Rachev
Keyword(s):  
Portfolio Optimization ◽  
Asset Allocation ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Selection Effect ◽  
Conditional Value At Risk ◽  
Positive Role ◽  
Performance Attribution ◽  
Dow Jones Industrial Average

This paper investigates performance attribution measures as a basis for constraining portfolio optimization. We employ optimizations that minimize conditional value-at-risk and investigate two performance attributes, asset allocation (AA) and the selection effect (SE), as constraints on asset weights. The test portfolio consists of stocks from the Dow Jones Industrial Average index. Values for the performance attributes are established relative to two benchmarks, equi-weighted and price-weighted portfolios of the same stocks. Performance of the optimized portfolios is judged using comparisons of cumulative price and the risk-measures: maximum drawdown, Sharpe ratio, Sortino–Satchell ratio and Rachev ratio. The results suggest that achieving SE performance thresholds requires larger turnover values than that required for achieving comparable AA thresholds. The results also suggest a positive role in price and risk-measure performance for the imposition of constraints on AA and SE.

scholarly journals A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hamid Reza Erfanian ◽  
M. H. Noori Skandari ◽  
A. V. Kamyad
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Nonsmooth Equations ◽  
Smooth Functions ◽  
Generalized Derivative ◽  
Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

scholarly journals Dynamic portfolio optimization with transaction costs and state-dependent drift

2015 ◽  
Vol 243 (3) ◽  
pp. 921-931 ◽  
Author(s):  
Jan Palczewski ◽  
Rolf Poulsen ◽  
Klaus Reiner Schenk-Hoppé ◽  
Huamao Wang
Keyword(s):  
Transaction Costs ◽  
Portfolio Optimization ◽  
State Dependent ◽  
Dynamic Portfolio ◽  
Dynamic Portfolio Optimization

High transparency flexible sensor for pressure and proximity sensing

2018 ◽  
Vol 32 (32) ◽  
pp. 1850394 ◽  
Author(s):  
Dan Bu ◽  
Si Qi Li ◽  
Yun Ming Sang ◽  
Cheng Jun Qiu
Keyword(s):  
Indium Tin Oxide ◽  
Pressure Range ◽  
Piecewise Linear ◽  
High Sensitivity ◽  
Maximum Error ◽  
Piecewise Linear Function ◽  
Good Repeatability ◽  
Flexible Pressure Sensor ◽  
Human Finger ◽  
Proximity Sensing

A high-sensitivity and high-transmittance flexible pressure sensor is presented in this paper. Using polydimethylsiloxane (PDMS) sensing film to cover indium tin oxide (ITO) electrodes interdigitated on the polyethylene terephthalate (PET) substrate, an interdigital capacitance (IDC) structure is constructed. The pressure and proximity sensing characteristics of the fabricated IDC sensor are investigated. The experiment results show that the IDC sensor has the piecewise linear function in different pressure range, especially sensitive to the low-pressure range with the pressure sensitivity of 6.64 kPa[Formula: see text]. Moreover, it has a good repeatability with the maximum error rate of 2.73% and a high transmittance over 90% in the wavelength range from 400 nm to 800 nm. As a human finger approaches or leaves, the proximity sensing characteristic emerges, with a maximum sensing distance of about 20 cm.

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