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Warunki realizacji przepływów pieniężnych w ubezpieczeniach wielostanowych

100%
Dębicka J.
Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie
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2011
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issue 873
69-79
EN
A uniform approach to the analysis of policy conditions of the realisation of future cash flows arising from multi-state insurance contracts is presented. Multiple state modeling is a classical stochastic tool for designing and implementing insurance products. We focus on the discrete-time model, which treats insurance payments as being made at the end of time intervals. In such a situation, one of the ways to handle numerical calculations of premiums and reserves is to use a matrix notation. Benefits can sometimes be realised after the end of an insurance period and include a deferred period or stopping time. The aim of this paper is to comprise these conditions into matrix formulas for premiums and reserves (for multistate insurance contracts), both for the deterministic and stochastic interest rate. This approach will enable us to come away with a flexible tool for the analysis of profits of multistate insurance contracts and simplifythe implementation of numerical procedures. To that end, the set of policy conditions Γ is proposed. This set simplifies pointing out the time horizon for cash flows arising from insurance contracts and allows for the modification of matrices related to the multistate model and its probabilistic structure, cash flows, and discount function. It also allows us to take into account benefits realised after the end of an insurance period (and also comprises deferred period and stopping time).
2

Matrix approach to analysis of a portfolio of multistate insurance contracts

100%
Dębicka J.
Śląski Przegląd Statystyczny
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2012
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issue 10(16)
39-55
EN
This paper discusses the calculation of moments of cash value of future payment streams arising from portfolio of multistate insurance contracts, where the evolution of the insured risk and the interest rate are random. A matrix form for formulas for the first two moments of cash value of the stream of future payments for a portfolio of policies is derived. As an application formulas for insurance premiums are provided. The general theory is illustrated with a case where the rate of interest is modeled by a Wiener and an Ornstein-Uhlenbeck process.
3
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Jubileusz 70-lecia Katedry Statystyki Uniwersytetu Ekonomicznego we Wrocławiu (1950-2020)

100%
Dębicka J.
Śląski Przegląd Statystyczny
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2020
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issue 19 (25)
7-30
4
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Pricing Marriage Insurance with Mortality Dependence

51%
Dębicka J., Heilpern S., Marciniuk A.
Central European Journal of Economic Modelling and Econometrics
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2023
|
issue 1
31-64
EN
Accurate determination of the probability structure of the multistate model is significant from the valuation and profitability assessment of insurance contracts standpoint. This article aims to analyse the effect of spouses' future lifetime dependence on premiums and prospective reserves for marriage insurance contracts. As a result, under the assumptions that the evolution of the insured risk is described by a nonhomogeneous Markov chain and the dependence between spouses' future lifetime is modelled by the copula, we derive formulas for the elements of the transition matrices. Based on actual data, we conduct a comparative analysis of actuarial values for three scenarios related to future lifetimes of husband and wife. We test the robustness of premium value to the changing degree of dependency between spouses' future lifetimes.
5
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Proposed solutions to increase the reliability and goodness of fit of the Thurstone method

51%
Dębicka J., Mazurek E., Ostasiewicz K.
Wiadomości Statystyczne. The Polish Statistician
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2024
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vol. 69
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issue 11
1-17
PL
Metoda Thurstone’a jest metodą agregacji preferencji, pozwalającą na porządko- wanie obiektów na skali interwałowej, w odróżnieniu od innych metod agregacji, za pomocą których otrzymuje się jedynie skalę porządkową. Trudno jednak traktować skalę interwałową uzyskaną przy użyciu metody Thurstone’a jako wiarygodną, ponieważ – jak pokazano w artykule – jest ona bardzo podatna na zależność od nieistotnych alternatyw: względna kolejność dwóch obiektów może zależeć od obecności innego, zupełnie niezależnego obiektu w badanym zbiorze. W artykule poruszono również kwestię wyrażenia, które ma podlegać minimalizacji. Thurstone wskazał wyrażenie, które można łatwo zminimalizować za pomocą stablicowanych wartości rozkładu normalnego. Jednak wobec obecnych mocy obliczeniowych komputerów możliwe jest minimalizowanie innego wyrażenia, które daje lepszą dobroć dopasowania częstości obserwowanych do oczekiwanych oraz pozwala uniknąć problemu dotyczącego częstości empirycznych bliskich 1. Artykuł ma na celu zaproponowanie dwóch ulepszeń metody Thurstone’a. Pierwszym jest stosowanie zgrubnej reguły dotyczącej progowej odległości między obiektami (w wielo- krotnościach odchylenia standardowego), poniżej której uporządkowanie obiektów nie może być uważane za rzetelne, oraz metody empirycznego badania stabilności porządku obiektów. Drugie polega na minimalizowaniu wyrażenia innego niż oryginalne, w szczególności gdy wśród częstości empirycznych występują bardzo wysokie wartości.
EN
The Thurstone method is a method of aggregation of preferences that leads to ordering objects at an interval scale, in contrast to other methods of aggregation, the application of which results in obtaining the ordinal scale only. However, we demonstrate that the interval scale obtained by means of the Thurstone method is not fully reliable, as it is strongly susceptible to the problem of irrelevant alternatives, i.e., the order of two objects might be dependent on whether there is or not a third, completely independent object in the studied collectivity. The other issue examined in the paper is the formula that is to be minimised in the Thurstone method. Thurstone proposed a formula easy to be minimised with tabularised values of normal distribution. However, today’s calculation powers of computers make it possible to minimise another formula, which allows a better fit of observed frequencies to the predicted ones, and makes it possible to avoid the problem with empirical frequencies close to 1. The aim of the paper is to propose two improvements to the Thurstone method. The first one involves the application of the rule of thumb to the minimal spacing (in terms of standard deviations), below which the ordering of objects cannot be regarded as reliable, and the use of the method of empirical examining of the stability of order. The second of the proposed improvements consists in minimising a formula other than the original one, especially in the cases where empirical frequencies reach very high values.
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