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Transactional Interpretation and the Generalized Poisson Distribution.

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Summary
This summary is machine-generated.

This study explores a quantum-like market approach using squeezed coherent states to define risk. It introduces a generalized Poisson distribution and a "risk of risk" concept for better strategy characterization.

Keywords:
Fisher informationFourier transformSchrödinger-like equationmarketquantum computerrisksqueezed coherent statessupply and demand

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Area of Science:

  • Quantitative Finance
  • Quantum Mechanics
  • Information Theory

Background:

  • Traditional market models often fail to capture complex risk dynamics.
  • Quantum principles offer novel frameworks for financial analysis.
  • Fisher information quantifies statistical distinguishability and is key to uncertainty.

Purpose of the Study:

  • To investigate a quantum-like market description using the principle of minimum Fisher information.
  • To assess the viability of squeezed coherent states as financial strategies.
  • To develop a quantum-based framework for market risk analysis.

Main Methods:

  • Representing squeezed coherent states using eigenvectors of market risk.
  • Deriving probability formulas for state representation.
  • Defining a generalized Poisson distribution for quantum risk.
  • Calculating total risk and introducing a "risk of risk" metric.

Main Results:

  • A generalized Poisson distribution is established, linking squeezed coherent states to quantum risk.
  • Formulas for total risk and the "risk of risk" (second central moment) are derived.
  • The "risk of risk" provides a numerical characterization of strategy risk.

Conclusions:

  • Quantum-like approaches, specifically using squeezed coherent states, offer a novel perspective on market risk.
  • The generalized Poisson distribution and "risk of risk" concept provide valuable tools for financial strategy analysis.
  • This framework has potential interpretations related to uncertainty relations in quantum mechanics.