actuarial mathematics
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2021 ◽  
Vol 2131 (2) ◽  
pp. 022107
Author(s):  
O Rusakov ◽  
Yu Yakubovich

Abstract Weconsider a PSI-process, that is a sequence of random variables (&), i = 0.1,…, which is subordinated by a continuous-time non-decreasing integer-valued process N(t): <K0 = ÇN(ty Our main example is when /V(t) itself is obtained as a subordination of the standard Poisson process 77(s) by a non-decreasing Lévy process S(t): N(t) = 77(S(t)).The values (&)one interprets as random claims, while their accumulated intensity S(t) is itself random. We show that in this case the process 7V(t) is a compound Poisson process of the stuttering type and its rate depends just on the value of theLaplace exponent of S(t) at 1. Under the assumption that the driven sequence (&) consists of i.i.d. random variables with finite variance we calculate a correlation function of the constructed PSI-process. Finally, we show that properly rescaled sums of such processes converge to the Ornstein-Uhlenbeck process in the Skorokhod space. We suppose that the results stated in the paper mightbe interesting for theorists and practitioners in insurance, in particular, for solution of reinsurance tasks.


Risks ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 139
Author(s):  
Corina Constantinescu ◽  
Julia Eisenberg

The Special Issue aims to highlight the interaction between actuarial and financial mathematics, which, due to the recent low interest rates and implications of COVID-19, requires an interlace between actuarial and financial methods, along with control theory, machine learning, mortality models, option pricing, hedging, unit-linked contracts and drawdown analysis, among others [...]


Author(s):  
O. I. Vasylyk ◽  
I. I. Lovytska

In the paper, we consider the problem of simulation of a strictly φ-sub-Gaussian generalized fractional Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly φ-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when φ(x) = (|x|^p)/p, |x| ≥ 1, p > 1. In order to obtain these results, we use some results from the theory of φ-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.


2020 ◽  
Vol 2 (6) ◽  
pp. 08-13
Author(s):  
Mohd Zaki Awang Chek ◽  
Isma Liana Ismail ◽  
Nur Faezah Jamal

The Massive Open Online Courses (MOOCs) is a new online learning platform that provides training beyond the classroom based on casual and social learning. Current learning methods that use PowerPoint slides usually bore students who would easily lose focus on their learning. MOOCs provide a new era of learning style with various learning methods. Using attractive notes with the aid of video, animation, and a variety of activities to promote a better learning environment adaptively. It is accessible anytime, anywhere, and gives flexibility to students in managing their learning routine. Therefore, UiTM Perak (Tapah Campus) has taken an initiative to implement MOOCs in one of the diploma subjects which is “Introduction to Actuarial Mathematics” (ASC305). Actuarial Mathematics is a subject taught under the actuarial science program in preparation for the professional actuarial examination under the Society of Actuaries (SOA), as well as getting students to understand the actuarial aspects of the current life insurance system. On top of that, this MOOC has encouraged worldwide participants where one will have experience in practicing their fundamental knowledge on each topic. The real-time communication between the instructor and participants for knowledge sharing, brainstorming, and exchanging opinions create a positive ambiance of "classroom-beyond-borders". Using MOOCs for the course opens great opportunities for instructors to be creatively and innovatively involved in preparing attractive content, learning activities, and hands-on assessments that suit all learning styles (auditory, visual, reading and writing, and kinesthetics). Thus, this paper illustrates and describes the development of Introduction to Actuarial Mathematics using MOOCs (https://ufuture.uitm.edu.my/courses/summary/ASC305).


2020 ◽  
Vol 3 (1) ◽  
pp. 45-50
Author(s):  
Azizah Azizah ◽  
Sapti Wahyuningsih

This research was conducted to analyze the test instruments used to measure the ability of students in actuarial mathematics courses in mathematics department, State University of Malang. Participants in this course consist of 40 students. The form of questions given were  multiple choice questions totaling 50 items related to the premium calculation material on life insurance. The Rasch model is used to get fit items. This analysis is carried out with the help of Winsteps software. From the Winsteps program output, 25 items were obtained fit to the Rasch model with an average MNSQ Outfit score for person and item 0.98 and 0.98, respectively. While the Outfit ZSTD value for person and item are 0 and -0.01 respectively. While the reliability of the instrument stated in alpha cronbach is 0.85


2020 ◽  
Vol 56 (1) ◽  
pp. 58-67
Author(s):  
Yu. M. Ermoliev ◽  
V. I. Norkin ◽  
B. V. Norkin

2019 ◽  
Author(s):  
David C. M. Dickson ◽  
Mary R. Hardy ◽  
Howard R. Waters

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