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Extended reduced-form framework for non-life insurance

Part of: Mathematical finance Stochastic analysis

Published online by Cambridge University Press:  14 June 2022

Francesca Biagini Open the ORCID record for Francesca Biagini [Opens in a new window]  and
Yinglin Zhang
Francesca Biagini*
Affiliation:
LMU Munich
Yinglin Zhang*
Affiliation:
LMU Munich
*
*Postal address: Department of Mathematics, LMU Munich, Theresienstraße, 39, 80333 Munich, Germany.
*Postal address: Department of Mathematics, LMU Munich, Theresienstraße, 39, 80333 Munich, Germany.
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Abstract

In this paper we propose a general framework for modeling an insurance liability cash flow in continuous time, by generalizing the reduced-form framework for credit risk and life insurance. In particular, we assume a nontrivial dependence structure between the reference filtration and the insurance internal filtration. We apply these results for pricing and hedging non-life insurance liabilities in hybrid financial and insurance markets, while taking into account the role of inflation under the benchmarked risk-minimization approach. This framework offers at the same time a general and flexible structure, and an explicit and treatable pricing-hedging formula.

Keywords

Non-life insurancereduced-form frameworkmarked point processbenchmark approachfiltration dependencemarket-consistent valuationrisk mitigation

MSC classification

Primary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 3 , September 2022 , pp. 945 - 973
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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