Dynamics of state-wise prospective reserves in the presence of non-monotone information
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Dynamics of state-wise prospective reserves in the presence of non-monotone information. / Christiansen, Marcus C.; Furrer, Christian.
I: Insurance: Mathematics and Economics, Bind 97, 2021, s. 81-98.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Dynamics of state-wise prospective reserves in the presence of non-monotone information
AU - Christiansen, Marcus C.
AU - Furrer, Christian
PY - 2021
Y1 - 2021
N2 - In the presence of monotone information, the stochastic Thiele equation describing the dynamics of state-wise prospective reserves is closely related to the classic martingale representation theorem. When the information utilized by the insurer is non-monotone, the classic martingale theory does not apply. By taking an infinitesimal approach, we derive a generalized stochastic Thiele equation that allows for information discarding. En passant, we solve some open problems for the classic case of monotone information. The results and their implication in practice are illustrated via examples where information is discarded upon and after stochastic retirement.
AB - In the presence of monotone information, the stochastic Thiele equation describing the dynamics of state-wise prospective reserves is closely related to the classic martingale representation theorem. When the information utilized by the insurer is non-monotone, the classic martingale theory does not apply. By taking an infinitesimal approach, we derive a generalized stochastic Thiele equation that allows for information discarding. En passant, we solve some open problems for the classic case of monotone information. The results and their implication in practice are illustrated via examples where information is discarded upon and after stochastic retirement.
KW - Infinitesimal martingales
KW - Life insurance
KW - Marked point processes
KW - Stochastic retirement
KW - Stochastic Thiele equations
UR - http://www.scopus.com/inward/record.url?scp=85100023768&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2021.01.005
DO - 10.1016/j.insmatheco.2021.01.005
M3 - Journal article
AN - SCOPUS:85100023768
VL - 97
SP - 81
EP - 98
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
ER -
ID: 256677127