Heterogeneity and uncertainty in a multistate framework
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Heterogeneity and uncertainty in a multistate framework D. Tabakova1 · E. Pitacco2 Received: 22 January 2020 / Accepted: 19 August 2020 © The Author(s) 2020
Abstract This research develops the scheme proposed in the paper Pollard [J Inst Actuar 96(2): 251–264, 1970], which is based on a two-state model for the analysis of 1-year mortality, but the results are also valid for the probabilities related to other types of insurance events such as disablement and accidents. We extend the Pollard’s original scheme into time-discrete models with more states (active-invalid-dead) together with further investigation into multi-year time horizon. Additionally, hypotheses for real-valued individual frailty are assumed in the models. As the baseline probabilistic structure, we have adopted a traditional three-state model in a Markov context. We focus on an insurance portfolio. Our outputs of interest are based on the probability distributions of the annual payouts for term insurance policies providing lump sum benefits both in case of death and in case of permanent disability. The analysis of the probability distributions allows us to assess the risk profile of the insurance portfolio, and thus to suggest appropriate actions in terms of premiums and capital allocation. In this regards, we adopt the percentile principle. Keyword Disability benefits · Death benefits · Frailty · Uncertainty · Markov chain Mathematics Subject Classification 60J20 · 62P05
The present paper reports the main achievements of the PhD thesis of D.Y. Tabakova, Co-supervisor prof. E. Pitacco.
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E. Pitacco [email protected] D. Tabakova [email protected]
1
MIB Trieste School of Management, Trieste, Italy
2
University of Trieste, Trieste, Italy
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D. Tabakova, E. Pitacco
1 Introduction The use of multistate models and, in particular, of Markov structures to represent the biometric features of insurance products in the area of insurance of the person can be dated back to the seminal contribution by Hoem (1969). Later contributions to life insurance and related fields, based on multistate models, are given by Amsler (1988), Hoem (1988) and Waters (1984). Moving to actuarial textbooks which present the actuarial structure of life and health insurance contracts in terms of multistate models, we quote (Haberman and Pitacco 1999; Norberg 2002) and, as specifically regards long-term care insurance, Denuit et al. (2019). Health insurance, and, more specifically disability insurance are presented by Pitacco (2014). The value of disability insurance from an economic perspective is addressed for example by Chandra and Samwick (2009). As noted by Pitacco (2019), heterogeneity of a population in respect of mortality (and disability) is due to differences among the individuals, which are caused by various risk factors. Some risk factors are observable, while others are unobservable. The set of observable risk factors clearly depends on the type of population addressed. It follows that the scientific and technical literature dealing with het
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