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Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

Standard Entropy Change for a Reaction

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...

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Option Portfolio Selection with Generalized Entropic Portfolio Optimization.

Peter Joseph Mercurio¹, Yuehua Wu¹, Hong Xie²

¹Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This summary is machine-generated.

Generalized Entropic Portfolio Optimization (GEPO) extends prior methods to handle mixed discrete and continuous returns in option strategies. This new framework optimizes portfolios for growth rate and relative entropy, outperforming traditional methods.

Keywords:

European options Kullback–Leibler divergence credit spreads iron condors option portfolios portfolio optimization portfolio selection relative entropy straddles strangles

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Area of Science:

Quantitative Finance
Computational Economics
Financial Engineering

Background:

Traditional portfolio optimization methods often struggle with the mixed discrete and continuous return profiles characteristic of option strategies.
Existing entropic portfolio optimization techniques have limitations when applied to complex option portfolios.
The need for a robust framework to optimize option portfolios based on growth rate and risk is critical.

Purpose of the Study:

To introduce Generalized Entropic Portfolio Optimization (GEPO), a novel method for selecting option portfolios.
To extend discrete entropic portfolio optimization (DEPO) to accommodate continuous returns, enabling application to diverse option strategies.
To provide mathematical tools for selecting efficient option portfolios using growth rate and relative entropy.

Main Methods:

Developed GEPO by generalizing DEPO to incorporate intervals of continuous returns.
Applied GEPO to a variety of option strategies, including covered calls, married puts, credit spreads, straddles, strangles, butterfly spreads, and iron condors.
Utilized portfolio growth rate and relative entropy as key performance metrics for optimization.

Main Results:

GEPO successfully accommodates option strategies with mixed discrete and continuous returns.
Demonstrated GEPO's applicability to a wide array of complex option portfolio constructions.
Empirical application to real market data showed GEPO outperforming the traditional Kelly criterion.

Conclusions:

GEPO offers an adaptable and mathematically sound framework for optimizing option portfolios.
The method is particularly well-suited for strategies where performance is best measured by portfolio growth rate.
GEPO represents a significant advancement in portfolio selection for options, offering superior performance compared to established methods.