Parallels between Quantum Mechanics and Insurance. Welcome the Quantum Actuary

Quantum mechanics, a fundamental theory in modern physics, has found applications in various fields. Surprisingly, it can also shed light on insurance markets and actuarial science. In this article, we explore how quantum concepts can enhance our understanding of risk, probability, and pricing in insurance. Quantum theory is one of the significant concept in modern physics. Many phenomena in nature and society also show the characteristics of "quantization", of course including the insurance market. Probability is the cornerstone in the actuarial calculation while the quantum mechanics could give different perspectives on the probability. There is a new approach to explore the quantum application to the insurance market by solving the partial differential equation of the Schr?dinger equation with some simple Hamiltonian such as infinite square potential well, potential barrier penetration and harmonic oscillator which may be helpful for the development of quantum actuarial.

Quantum mechanics is an important concept in modern physics, which was proposed by Max Planck in 1900. He found that radiant energy is discontinuous and can only be taken as an integral multiple of the unit of energy. Later research shows that not only does energy show this discontinuous separation property, but other physical quantities such as angular momentum, spin, and charge also show this discontinuous quantization phenomenon, which is fundamentally different from classical physics represented by Newtonian mechanics. If a physical quantity has the smallest unit and cannot be separated continuously, it can be said that the physical quantity is quantized, and the smallest basic unit is called quantum. Many phenomena in nature and society show the characteristics of “quantization,” of course including the insurance market.

Probability is the cornerstone in the actuarial calculation while the quantum mechanics could give different perspectives on the probability. Just like force, mass, acceleration, energy, and momentum in classical mechanics are continuous deterministic variables, actuarial variables, such as premium, claim, profit, expense, and distribution earning, are also considered to be continuous deterministic variables. In quantum theory, when several particles interact with each other, due to the properties of each particle having been integrated into a whole property, it is impossible to describe the properties of each particle alone, but only the properties of the whole system, which is called quantum entanglement.

In the insurance field, there also exists the phenomenon of quantum entanglement. The reason why insurance can be priced and provide risk protection is not based on the individual risk probability, but the overall risk probability. In the face of a complex and changeable quantized insurance market, traditional actuarial theory may lack effective explanatory and predictive power. Each policy can be regarded as the smallest unit and cannot be separated continuously, so it can be said that each policy is similar as the quantum and have the quantum property. In this article, we start from a new approach to explore the quantum application to the insurance market by using some simple Hamiltonian operators. By solving the corresponding partial differential equation, insurance phenomena could be quantitatively described under the new framework of quantum actuarial theory.

Quantum Actuarial Approach

To apply quantum principles to insurance, there needs to be a new approach:

1. Hamiltonian Operators: We use simple Hamiltonian operators (such as infinite square potential wells, potential barriers, and harmonic oscillators) to describe insurance phenomena.
2. Schr?dinger Equation: By solving the Schr?dinger equation (a partial differential equation), we quantitatively describe insurance events within this quantum framework.
3. Quantum Entanglement: Just as particles become entangled in quantum systems, insurance policies are interconnected. Pricing and risk assessment rely on overall probabilities rather than individual risks.

Examples of Quantum Actuarial Calculations

1. Ruin Probability: Applying quantum concepts, we can model the ruin probability of an insurance company.
2. Solvency and Reserves: Quantum mechanics informs solvency assessments and equalization reserves.
3. Reinsurance Optimization: Quantum-inspired approaches can enhance reinsurance strategies.
4. Catastrophe Modeling: Quantum techniques may improve catastrophe risk modeling

While quantum actuarial theory is still in its infancy, exploring this novel approach could revolutionize insurance pricing, risk management, and policy analysis. As we continue to bridge the gap between quantum mechanics and actuarial science, we unlock new insights into the complex world of insurance.

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