The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson in J Financ Quant Anal 18(1):141–148 (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical regression. The method can be adapted to general diffusion processes as long as quick and accurate pricing methods exist for the corresponding European and perpetual American options. The American option price is shown to be approximately equal to an interpolation of two European option prices with the interpolation weight proportional to a perpetual American option. In the Black-Scholes model, our method achieves the same efficiency as the quadratic approximation of Barone-Adesi and Whaley in J Financ 42:301–320 (1987), with our method being generally more accurate for out-of-the-money and long-maturity options. When applied to Heston’s stochastic volatility model, our method is shown to be extremely efficient and fairly accurate.

In the present paper, the maximal Lyapunov exponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invariant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the analytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behaviors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular boundaries for one-dimensional phase diffusion process, analytical expressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.

A Closed-Form Solution to American Options under General Diffusions

Since diffusion processes arise in so many different fields, efficient technics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For efficiency reasons, it is particularly challenging to simulate directly this hitting time by avoiding to construct the whole paths. In the Brownian case, the distribution of the first-passage time is explicitly known and can be easily used for simulation purposes. The authors introduce a new rejection sampling algorithm which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes. The efficiency of the method, which is essentially based on Girsanov’s transformation, is described through theoretical results and numerical examples.

Aspects of prospective mean values in risk theory

Special symmetry conditions on the transition p.d.f. of one-dimensional time-homogeneous diffusion processes with natural boundaries are investigated and exploited to derive closed-form results concerning the transition p.d.f.'s in the presence of absorbing and reflecting boundaries and the first-passage-time p.d.f. through time-dependent boundaries.

The diffusion of a suspended brownian particle along a sinusoidally corrugated narrow channel is investigated to assess the validity of two competing analytical schemes, both based on effective one-dimensional kinetic equations, one continuous (entropic channel scheme) and the other discrete (random walker scheme). For narrow pores, the characteristic diffusion time scale is represented by the mean first exit time out of a channel compartment. Such a diffusion time has been analytically calculated in both approximate schemes; the two analytical results coincide in leading order and are in excellent agreement with the simulation data.

The article examines the essence and strategic directions of digitalization in the financial and insurance services market. It is established that digitalization in the financial and insurance sectors is not only a technological trend, but also a key factor in strategic development. The rapid development of modern technologies significantly affects the financial and insurance services market, changing both the financial products themselves and the principles of their use and distribution methods. In today's conditions of global digitalization of the world, the dynamic development of the country's economy and financial market requires the implementation of an effective mechanism for their functioning and the use of a set of innovative scientific approaches. It is proven that in today's conditions, the digitalization of financial and insurance services means the transition from traditional forms of service to the implementation of the latest electronic technologies. The article defines the essence and analyzes the Digital Transformation Index of Ukraine. In Ukraine, the digitalization of the financial and insurance market is becoming a driving force for the transformation of financial practices and increasing the efficiency of financial process management. This contributes to increasing the availability and quality of services, reducing their cost for consumers, and the overall development of the financial sector. A study of the key components of InsurTech was conducted and it was found that the advantages of this type of insurance are convenience in registration, minimization of papers and availability anywhere in the world. It was determined that FinTech is a set of innovative digital technologies used to carry out financial activities and provide financial services. In the insurance services market, in the context of digitalization, the InsurTech direction has become relevant as a modern form of providing insurance services in an online environment. In the context of strategic directions of digitalization in the financial and insurance services market, we note that the key ones are the implementation of digital identification and the implementation of electronic document management, the development of FinTech and InsurTech, the transition to cloud technologies and the strengthening of cybersecurity and personal data protection. Further expansion of the integration of FinTech and InsurTech solutions into the financial ecosystem is expected in the near future.

This paper investigates portfolio selection and risk control between individuals and an insurer in a frame of stochastic Stackelberg differential game. In the Stackelberg game, the insurer plays as the leader who determines the price of insurance, and individuals play as the followers deciding how much insurance they should buy. On one hand, we suppose that there are homogeneous individuals in the market who can purchase insurance from one insurer. Each individual aims to achieve optimal consumption, insurance, and investment policies while considering premium prices and the performance of financial market. On the other hand, the insurer can adjust premium prices and investment policies in response to the individuals' insurance demands and the performance of financial market. Both individuals and the insurer aim to maximize their expectation of utilities. By employing the dynamic programming principle, we obtain closed‐form solutions for optimal policies and value functions. The results show that the correlation between financial market and insurance market has a significant impact on the optimal strategy. A strong negative correlation would lead to an inefficient insurance market, but full insurance demand occurs for strong positive correlated markets. Most interestingly, our result indicates that insurance demand can effectively increase individuals consumption level and investment level on risk assets for positive correlated markets. Finally, we also find the equilibrium insurance price decreases and the equilibrium insurance demand increases with respect to the size of insurance market for positive correlated markets.

Страховой рынок является неотъемлемым элементом российского финансового сектора. В национальной экономике страхование выступает одним из финансовых инструментов, обеспечивающих эффективную защиту имущественных интересов физических и юридических лиц от различных рисков. В статье проводится оценка современного состояния и развития страхового рынка в России. Анализируется структура страхового рынка Российской Федерации по отраслям страхования, инвестиционная деятельность страховых компаний на финансовом рынке. В результате проведенного анализа выделены основные проблемы развития российского страхового рынка и представлены рекомендации по улучшению его состояния. The insurance market is an integral element of the Russian financial sector. In the national economy, insurance is one of the financial instruments that provide effective protection of the property interests of individuals and legal entities against various risks. The article assesses the current state and development of the insurance market in Russia. The structure of the insurance market of the Russian Federation is analyzed by branches of insurance, the investment activity of insurance companies in the financial market. As a result of the analysis, the main problems of the development of the Russian insurance market are identified and recommendations are presented for improving its condition.

The insurance market in Albania has been started to operate in the last years of centralized socialist system. It was represented by state insurance Company INSIG. It was the first important segment of the financial market to develop faster once Albania entered into the free market economy model on the last decade of the past century. It is the largest and most advanced market in non-banking financial sector. Together with investment funds, pension funds securities markets those are under the supervision of Albanian Financial Supervision Authority, not Central Bank. The insurance market, has had a lot development and positive growth in terms of wide range of products offer and the geographically expansion all over the country and in some neighboring countries in the Balkan region where Albanian population live. This potential is based on the favorable economic conditions, improved regulatory and supervisory system, low market penetration rate, as well as, on business community and population, which are dynamic and easily adaptable. The Insurance Industry has been undergoing dramatic changes during the last ten years. This industry can help the business companies and other entities on having economic and financial support, mitigating their risks and losses as well from natural disasters or other uncertainties. This sector can give a good support on social development and financial contribution on economy by reducing the risk of future losses. There are a lot of empirical research based on financial analyses of Albanian Insurance Companies in which you can see a causal relationship between insurance sector effects in economic growth by bearing risk on business investment. The study of qualitative and quantitative information on Main Insurance Company in Albania, their business model and risk drivers shows the development stage and challenges and steps needs to be in line with EU directives. Incorporation of international best practices combined with an efficient regulatory and supervisory approach will certainly play a very big role in the non-banking financial market development and growth.

Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first passage time, is an active area of research relevant to many disciplines. Exact results for the mean first passage time for diffusion on simple geometries, such as lines, discs and spheres, are well-known. In contrast, computational methods are often used to study the first passage time for diffusion on more realistic geometries where closed-form solutions of the governing elliptic boundary value problem are not available. Here, we develop a perturbation solution to calculate the mean first passage time on irregular domains formed by perturbing the boundary of a disc or an ellipse. Classical perturbation expansion solutions are then constructed using the exact solutions available on a disc and an ellipse. We apply the perturbation solutions to compute the mean first exit time on two naturally-occurring irregular domains: a map of Tasmania, an island state of Australia, and a map of Taiwan. Comparing the perturbation solutions with numerical solutions of the elliptic boundary value problem on these irregular domains confirms that we obtain a very accurate solution with a few terms in the series only. MATLAB software to implement all calculations is available at https://github.com/ProfMJSimpson/Exit_time.

General References, Diffusion Processes, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion Processes, Electromigration, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion Processes, Electromigration, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction