Warunki realizacji przepływów pieniężnych w ubezpieczeniach wielostanowych
General Actuarial Aspects of Policy Conditions for Multistate Insurance Contracts

Summary/Abstract: 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).

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