scholarly journals Portfolio Optimization for Binary Options Based on Relative Entropy

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 752 ◽  
Author(s):  
Peter Joseph Mercurio ◽  
Yuehua Wu ◽  
Hong Xie
Keyword(s):  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Relative Entropy ◽  
Asset Allocation ◽  
Optimization Problem ◽  
General Setting ◽  
Short Term ◽  
Kelly Criterion ◽  
Portfolio Returns ◽  
Binary Options

The portfolio optimization problem generally refers to creating an investment portfolio or asset allocation that achieves an optimal balance of expected risk and return. These portfolio returns are traditionally assumed to be continuous random variables. In An Entropy-Based Approach to Portfolio Optimization, we introduced a novel non-parametric optimization method based on Shannon entropy, called return-entropy portfolio optimization (REPO), which offers a simple and fast optimization algorithm for assets with continuous returns. Here, in this paper, we would like to extend the REPO approach to the optimization problem for assets with discrete distributed returns, such as those from a Bernoulli distribution like binary options. Under a discrete probability distribution, portfolios of binary options can be viewed as repeated short-term investments with an optimal buy/sell strategy or general betting strategy. Upon the outcome of each contract, the portfolio incurs a profit (success) or loss (failure). This is similar to a series of gambling wagers. Portfolio selection under this setting can be formulated as a new optimization problem called discrete entropic portfolio optimization (DEPO). DEPO creates optimal portfolios for discrete return assets based on expected growth rate and relative entropy. We show how a portfolio of binary options provides an ideal general setting for this kind of portfolio selection. As an example we apply DEPO to a portfolio of short-term foreign exchange currency pair binary options from the NADEX exchange platform and show how it outperforms leading Kelly criterion strategies. We also provide an additional example of a gambling application using a portfolio of sports bets over the course of an NFL season and present the advantages of DEPO over competing Kelly criterion strategies.

Portfolio Optimization and Asset Allocation With Metaheuristics

2021 ◽  
pp. 78-96
Author(s):  
Jhuma Ray ◽  
Siddhartha Bhattacharyya ◽  
N. Bhupendro Singh
Keyword(s):  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Asset Allocation ◽  
Value At Risk ◽  
Optimal Allocation ◽  
Short Note ◽  
Objective Functions ◽  
Cardinality Constraints ◽  
Distribution Of Wealth ◽  
Risk Optimization

Portfolio optimization stands to be an issue of finding an optimal allocation of wealth to place within the obtainable assets. Markowitz stated the problem to be structured as dual-objective mean-risk optimization, pointing the best trade-off solutions within a portfolio between risks which is measured by variance and mean. Thus the major intention was nothing else than hunting for optimum distribution of wealth over a specific amount of assets by diminishing risk and maximizing returns of a portfolio. Value-at-risk, expected shortfall, and semi-variance measures prove to be complex for measuring risk, for maximization of skewness, liquidity, dividends by added objective functions, cardinality constraints, quantity constraints, minimum transaction lots, class constraints in real-world constraints all of which are incorporated in modern portfolio selection models, furnish numerous optimization challenges. The emerging portfolio optimization issue turns out to be extremely tough to be handled with exact approaches because it exhibits nonlinearities, discontinuities and high-dimensional, efficient boundaries. Because of these attributes, a number of researchers got motivated in researching the usage of metaheuristics, which stand to be effective measures for finding near optimal solutions for tough optimization issues in an adequate computational time frame. This review report serves as a short note on portfolio optimization field with the usage of Metaheuristics and finally states that how multi-objective metaheuristics prove to be efficient in dealing with portfolio selection problems with complex measures of risk defining non-convex, non-differential objective functions.

IMPLICATION OF THE KELLY CRITERION FOR MULTI-DIMENSIONAL PROCESSES

2010 ◽  
Vol 13 (01) ◽  
pp. 93-112 ◽  
Author(s):  
YINGDONG LV ◽  
BERNHARD K. MEISTER
Keyword(s):  
Financial Markets ◽  
Diffusion Processes ◽  
General Setting ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Short Term ◽  
Kelly Criterion ◽  
Optimal Investment Strategy ◽  
Risk Free Rate ◽  
Free Rate

In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio in terms of drift, short term risk-free rate and correlations for a set of generic multi-dimensional diffusion processes satisfying some simple conditions. Properties of the optimal investment strategy are studied. The paper ends with a short discussion of the implications of these ideas for financial markets.

scholarly journals Option Portfolio Selection with Generalized Entropic Portfolio Optimization

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 805
Author(s):  
Peter Joseph Mercurio ◽  
Yuehua Wu ◽  
Hong Xie
Keyword(s):  
Growth Rate ◽  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Kelly Criterion ◽  
Optimization Framework ◽  
Wide Range ◽  
Option Strategies ◽  
Real Market ◽  
Efficient Option ◽  
Ideal Method

In this third and final paper of our series on the topic of portfolio optimization, we introduce a further generalized portfolio selection method called generalized entropic portfolio optimization (GEPO). GEPO extends discrete entropic portfolio optimization (DEPO) to include intervals of continuous returns, with direct application to a wide range of option strategies. This lays the groundwork for an adaptable optimization framework that can accommodate a wealth of option portfolios, including popular strategies such as covered calls, married puts, credit spreads, straddles, strangles, butterfly spreads, and even iron condors. These option strategies exhibit mixed returns: a combination of discrete and continuous returns with performance best measured by portfolio growth rate, making entropic portfolio optimization an ideal method for option portfolio selection. GEPO provides the mathematical tools to select efficient option portfolios based on their growth rate and relative entropy. We provide an example of GEPO applied to real market option portfolio selection and demonstrate how GEPO outperforms traditional Kelly criterion strategies.

scholarly journals Multi-Swarm Multi-Objective Optimizer Based on p-Optimality Criteria for Multi-Objective Portfolio Management

2019 ◽  
Vol 2019 ◽  
pp. 1-22 ◽  
Author(s):  
Yabao Hu ◽  
Hanning Chen ◽  
Maowei He ◽  
Liling Sun ◽  
Rui Liu ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Portfolio Optimization ◽  
Portfolio Management ◽  
Asset Allocation ◽  
Optimization Problem ◽  
Optimality Criteria ◽  
Investment Fund ◽  
Multi Objective ◽  
Portfolio Optimization Problem ◽  
Investment Portfolio Optimization

Portfolio management is an important technology for reasonable investment, fund management, optimal asset allocation, and effective investment. Portfolio optimization problem (POP) has been recognized as an NP-hard problem involving numerous objectives as well as constraints. Applications of evolutionary algorithms and swarm intelligence optimizers for resolving multi-objective POP (MOPOP) have attracted considerable attention of researchers, yet their solutions usually convert MOPOP to POP by means of weighted coefficient method. In this paper, a multi-swarm multi-objective optimizer based on p-optimality criteria called p-MSMOEAs is proposed that tries to find all the Pareto optimal solutions by optimizing all objectives at the same time, rather than through the above transforming method. The proposed p-MSMOEAs extended original multiple objective evolutionary algorithms (MOEAs) to cooperative mode through combining p-optimality criteria and multi-swarm strategy. Comparative experiments of p-MSMOEAs and several MOEAs have been performed on six mathematical benchmark functions and two portfolio instances. Simulation results indicate that p-MSMOEAs are superior for portfolio optimization problem to MOEAs when it comes to optimization accuracy as well as computation robustness.

Portfolio Optimization and Asset Allocation With Metaheuristics

2019 ◽  
pp. 1-26
Author(s):  
Jhuma Ray ◽  
Siddhartha Bhattacharyya ◽  
N. Bhupendro Singh
Keyword(s):  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Asset Allocation ◽  
Value At Risk ◽  
Optimal Allocation ◽  
Short Note ◽  
Objective Functions ◽  
Cardinality Constraints ◽  
Distribution Of Wealth ◽  
Risk Optimization

Portfolio optimization stands to be an issue of finding an optimal allocation of wealth to place within the obtainable assets. Markowitz stated the problem to be structured as dual-objective mean-risk optimization, pointing the best trade-off solutions within a portfolio between risks which is measured by variance and mean. Thus the major intention was nothing else than hunting for optimum distribution of wealth over a specific amount of assets by diminishing risk and maximizing returns of a portfolio. Value-at-risk, expected shortfall, and semi-variance measures prove to be complex for measuring risk, for maximization of skewness, liquidity, dividends by added objective functions, cardinality constraints, quantity constraints, minimum transaction lots, class constraints in real-world constraints all of which are incorporated in modern portfolio selection models, furnish numerous optimization challenges. The emerging portfolio optimization issue turns out to be extremely tough to be handled with exact approaches because it exhibits nonlinearities, discontinuities and high-dimensional, efficient boundaries. Because of these attributes, a number of researchers got motivated in researching the usage of metaheuristics, which stand to be effective measures for finding near optimal solutions for tough optimization issues in an adequate computational time frame. This review report serves as a short note on portfolio optimization field with the usage of Metaheuristics and finally states that how multi-objective metaheuristics prove to be efficient in dealing with portfolio selection problems with complex measures of risk defining non-convex, non-differential objective functions.

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 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.

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.

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