Ruin probability via several numerical methods

In this thesis, ruin probabilities of insurance companies are studied. Ruin proba- bility in finite time is considered because it is more realistic compared with infinite time ruin probabilities. However, infinite time methods are also mentioned in order to compare them with the finite time methods. The thesis will initially provide some information about ruin probability of a risk process in finite and infinite time, and then the Markov chain and quantum mechan- ics approaches will be shown in order to compute the ruin probability. Using a reinsurance agreement, which is a risk sharing tool in actuarial science, the ruin probability of a modified surplus process in finite time via the quantum mechanics approach is studied. Furthermore, some optimization problems about capital injections, withdrawals and reinsurance premiums are taken into considera- tion in order to minimise the ruin probability. Finally, the thesis compares the finite time method under the reinsurance agreement in terms of the ruin probability and total injections amount with an infinite time counterpart method

Accumulators and Bookmaker’s Capital with Perturbed Stochastic Processes

The sports betting industry has been growing at a phenomenal rate and has many similarities to the financial market in that a payout is made contingent on an outcome of an event. Despite this, there has been little to no mathematical focus on the potential ruin of bookmakers. In this paper, the expected profit of a bookmaker and probability of multiple soccer matches are observed via Dirac notations and Feynman’s path calculations. Furthermore, we take the unforeseen circumstances into account by subjecting the betting process to more uncertainty. A perturbed betting process, set by modifying the conventional stochastic process, is handled to scale and manage this uncertainty

Quantum Computing in Insurance Capital Modelling

This paper proposes a quantum computing approach for insurance capital modelling. Using an open-source software development kit, Qiskit, an algorithm for working on a superconducting type IBM quantum computer is developed and implemented to predict the capital of insurance companies in the classical surplus process. With the fundamental properties of quantum mechanics, Dirac notation and Feynman’s path calculation are shown. Furthermore, custom quantum insurance premium and claim gates are investigated in order to build a quantum circuit with respect to initial reserve, premium and claim amounts. Some numerical results are presented and discussed at the end of the paper

Optimal Reinsurance via Dirac-Feynman Approach

In this paper, the Dirac-Feynman path calculation approach is applied to analyse finite time ruin probability of a surplus process exposed to reinsurance by capital injections. Several reinsurance optimization problems on optimum insurance and reinsurance premium with respect to retention level are investigated and numerically illustrated. The retention level is chosen to decrease the finite time ruin probability and to guarantee that reinsurance premium covers an average of overall capital injections. All computations are based on Dirac-Feynman path calculation approach applied to the convolution type operators perturbed by Injection operator (shift type operator). In addition, the effect of the Injection operator on ruin probability is analysed

Examining the Effects of Gradual Catastrophes on Capital Modelling and the Solvency of Insurers: The Case of COVID-19

This paper models the gradual elements of catastrophic events on non-life insurance capital with a particular focus on the impact of pandemics, such as COVID-19. A combination of actuarial and epidemiological models are handled by the Markovian probabilistic approach, with Feynman’s path calculation and Dirac notations, in order to observe how a pandemic risk may affect an insurer via reduced business. We also examine how the effects of a pandemic can be taken into account both during and at the end of the process. Examples are also provided showing the potential effects of a pandemic on different types of insurance product

Cyber Risk in Insurance: A Quantum Modeling

In this research, we consider cyber risk in insurance using a quantum approach, with a focus on the differences between reported cyber claims and the number of cyber attacks that caused them. Unlike the traditional probabilistic approach, quantum modeling makes it possible to deal with non-commutative event paths. We investigate the classification of cyber claims according to different cyber risk behaviors to enable more precise analysis and management of cyber risks. Additionally, we examine how historical cyber claims can be utilized through the application of copula functions for dependent insurance claims. We also discuss classification, likelihood estimation, and risk-loss calculation within the context of dependent insurance claim data

A Quantum-Type Approach to Non-Life Insurance Risk Modelling

A quantum mechanics approach is proposed to model non-life insurance risks and to compute the future reserve amounts and the ruin probabilities. The claim data, historical or simulated, are treated as coming from quantum observables and analyzed with traditional machine learning tools. They can then be used to forecast the evolution of the reserves of an insurance company. The following methodology relies on the Dirac matrix formalism and the Feynman path-integral method

A Quantum-Type Approach to Non-Life Insurance Risk Modelling

International audienc

Using Spray Dried Sugar Bett Molasses in Ice Cream as a Novel Bulking Agent

In this study, it is aimed to investigate and evaluate the use of molasses which is a by-product of sugar production as a novel bulking agent in ice cream as a sugar replacer. Sugar beet molasses (75%) and 12 DE maltodextrin (25%) were converted into powder form by spray drying. Spray-dried sugar beet molasses (SDSM) was then used as a substitute of sugar in different ratios (0:100, 25:75, 50:50, 75:25 and 100:0) in the ice cream products. The increased amount of SDSM decreased the overrun, L*, whiteness index (WI) and melting behaviours and increased a*, b*, total phenolic content, consistency and viscosity. Meanwhile, thermal properties have not been affected by the use of SDSM (P < 0.05). The sensory find- ings have been particularly interesting especially when replacing above 50% sugar with SDSM, aroma, flavour and general acceptability decrease. According to the results of this study, substituting 25% of total sugar with SDSM as a bulking agent can decrease cost of the product and improve total phenolic content and some quality parameters without compromising sensorial propertie

A Quantum-Type Approach to Non-Life Insurance Risk Modelling

A quantum mechanics approach is proposed to model non-life insurance risks and to compute the future reserve amounts and the ruin probabilities. The claim data, historical or simulated, are treated as coming from quantum observables and analyzed with traditional machine learning tools. They can then be used to forecast the evolution of the reserves of an insurance company. The following methodology relies on the Dirac matrix formalism and the Feynman path-integral method