No Arbitrage in Insurance and the QP-Rule

Artzner, Philippe; Eisele, Karl-Theodor; Schmidt, Thorsten

doi:10.2139/ssrn.3607708

Cited by 12 publications

(14 citation statements)

References 36 publications

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“…For two probability measures Q (1) , Q (2) equivalent to P and a stopping time τ ≤ T , the probability measure…”

Section: The Valuation Framework 21 Preliminariesmentioning

confidence: 99%

“…is called the pasting of Q (1) and Q (2) in τ . It is often convenient to express the pasting Q (3) of Q (1) , Q (2) in τ in terms of the density processes D (1) , D (2) with respect to P,…”

Section: The Valuation Framework 21 Preliminariesmentioning

confidence: 99%

“…In Artzner et al [2] and Deelstra et al [8] it is argued that diversifiable insurance risk should only be assigned a value corresponding to the P-expectation of such risk since the law of large numbers applies if the insurance company may form arbitrarily large portfolios. In our setting this argument is not valid since the corporate entity to which the insurance company's aggregate liability is transferred is a separate entity (referred to as reference undertaking in Solvency II) that may not be merged with other corporate entities.…”

Section: Introductionmentioning

confidence: 99%

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Multiple-prior valuation of cash flows subject to capital requirements

Engsner¹,

Lindskog²,

Thoegersen³

2021

Preprint

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We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. Building on the theory on multiple-prior optimal stopping we propose a valuation functional with sound economic properties that applies to any liability cash flow. Whereas a replicable cash flow is assigned the market value of the replicating portfolio, a cash flow that is not fully replicable is assigned a value which is the sum of the market value of a replicating portfolio and a positive margin. The margin is a direct consequence of considering a hypothetical transfer of the liability cash flow from an insurance company to an empty corporate entity set up with the sole purpose to manage the liability run-off, subject to repeated capital requirements, and considering the valuation of this entity from the owner's perspective taking model uncertainty into account. Aiming for applicability, we consider a detailed insurance application and explain how the optimisation problems over sets of probability measures can be cast as simpler optimisation problems over parameter sets corresponding to parameterised density processes appearing in applications.

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“…For two probability measures Q (1) , Q (2) equivalent to P and a stopping time τ ≤ T , the probability measure…”

Section: The Valuation Framework 21 Preliminariesmentioning

confidence: 99%

Section: The Valuation Framework 21 Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiple-prior valuation of cash flows subject to capital requirements

Engsner¹,

Lindskog²,

Thoegersen³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In the present document we will deal with a way to calculate the share of each economic agent, be it the capital providers or shareholders or the insured through their extra premium. The problem on how to fix the total amount of regulatory capital is the subject of joint ongoing work, which was initiated by [2].…”

mentioning

confidence: 99%

“…Risk averseness is usually translated by concavity properties and it is believed that combinations are less risky than individual positions. This explains property (2). Property (3) means that risk adjusted valuations are measured in money units.…”

mentioning

confidence: 99%