Optimal reinsurance design under solvency constraints
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Optimal reinsurance design under solvency constraints. / Avanzi, Benjamin; Lau, Hayden; Steffensen, Mogens.
I: Scandinavian Actuarial Journal, Bind 2024, Nr. 4, 2024, s. 383–416.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Optimal reinsurance design under solvency constraints
AU - Avanzi, Benjamin
AU - Lau, Hayden
AU - Steffensen, Mogens
N1 - Publisher Copyright: © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
PY - 2024
Y1 - 2024
N2 - We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled ‘down’ via reinsurance, rather than ‘up’ via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the (Formula presented.) and (Formula presented.) measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated.
AB - We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled ‘down’ via reinsurance, rather than ‘up’ via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the (Formula presented.) and (Formula presented.) measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated.
KW - martingale method
KW - payoff function
KW - quadratic utility
KW - Reinsurance
KW - terminal value constraints
U2 - 10.1080/03461238.2023.2257405
DO - 10.1080/03461238.2023.2257405
M3 - Journal article
AN - SCOPUS:85173785379
VL - 2024
SP - 383
EP - 416
JO - Scandinavian Actuarial Journal
JF - Scandinavian Actuarial Journal
SN - 0346-1238
IS - 4
ER -
ID: 371023214