TY - JOUR
T1 - Reserves and cash flows under stochastic retirement
AU - Gad, Kamille Sofie Tågholt
AU - Nielsen, Jeppe Woetmann
PY - 2016/11/25
Y1 - 2016/11/25
N2 - Uncertain time of retirement and uncertain structure of retirement benefits are risk factors for life insurance companies. Nevertheless, classical life insurance models assume these are deterministic. In this paper, we include the risk from stochastic time of retirement and stochastic benefit structure in a classical finite-state Markov model for a life insurance contract. We include discontinuities in the distribution of the retirement time. First, we derive formulas for appropriate scaling of the benefits according to the time of retirement and discuss the link between the scaling and the guarantees provided. Stochastic retirement creates a need to rethink the construction of disability products for high ages and ways to handle this are discussed. We show how to calculate market reserves and how to use modified transition probabilities to calculate expected cash flows without significantly more complexity than in the traditional model. At last, we demonstrate the impact of stochastic retirement on market reserves and expected cash flow in numerical examples.
AB - Uncertain time of retirement and uncertain structure of retirement benefits are risk factors for life insurance companies. Nevertheless, classical life insurance models assume these are deterministic. In this paper, we include the risk from stochastic time of retirement and stochastic benefit structure in a classical finite-state Markov model for a life insurance contract. We include discontinuities in the distribution of the retirement time. First, we derive formulas for appropriate scaling of the benefits according to the time of retirement and discuss the link between the scaling and the guarantees provided. Stochastic retirement creates a need to rethink the construction of disability products for high ages and ways to handle this are discussed. We show how to calculate market reserves and how to use modified transition probabilities to calculate expected cash flows without significantly more complexity than in the traditional model. At last, we demonstrate the impact of stochastic retirement on market reserves and expected cash flow in numerical examples.
KW - behavioural option
KW - benefit scaling
KW - discontinuous transition probabilities
KW - ordinary differential equation
KW - Solvency II
UR - http://www.scopus.com/inward/record.url?scp=84927549403&partnerID=8YFLogxK
U2 - 10.1080/03461238.2015.1028432
DO - 10.1080/03461238.2015.1028432
M3 - Journal article
AN - SCOPUS:84927549403
SN - 0346-1238
VL - 10
SP - 876
EP - 890
JO - Scandinavian Actuarial Journal
JF - Scandinavian Actuarial Journal
ER -