Asset-liability management for long-term insurance business

Albrecher, Hansjörg; Bauer, Daniel J.; Embrechts, Paul; Filipović, Damir; Koch-Médina, Pablo; Korn, Ralf; Loisel, Stéphane; Pelsser, Antoon; Schiller, Frank; Schmeiser, Hato; Wagner, Joël

doi:10.1007/s13385-018-0167-5

Cited by 19 publications

(10 citation statements)

References 37 publications

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“…In that case, some (generally imperfect) hedging of S by Y is possible and typically a two-step approach is followed (see Möhr, 2011 andAlbrecher et al, 2018). First, the insurer determines a hedging portfolio that is as close as possible to the liability S. To measure "closeness" the quadratic loss function is generally used, providing a trading strategy θ S = (θ 0 , .…”

Section: Two-step Valuation With a Quadratic Loss Functionmentioning

confidence: 99%

Insurance Valuation: A Two-Step Generalised Regression Approach

Barigou¹,

Bignozzi²,

Tsanakas³

2021

ASTIN Bull.

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Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.

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Section: Two-step Valuation With a Quadratic Loss Functionmentioning

confidence: 99%

Insurance Valuation: A Two-Step Generalised Regression Approach

Barigou¹,

Bignozzi²,

Tsanakas³

2021

ASTIN Bull.

View full text Add to dashboard Cite

show abstract

“…Since Germany has ratified Article 91 of [12], we apply Theorem 4.2 in the form of estimates (4.38). 1 Unfortunately interest rate implied volatilities are not publicly available. Therefore, we fix an artificial volatility structure that approximately reflects the correct behavior (Section 5.A) and provide sensitivities with respect to this choice (Section 5.B).…”

Section: Application To Reported Valuesmentioning

confidence: 99%

“…All of the foregoing difficulties are characteristics of traditional life insurance, and the corresponding market consistent valuation is a relatively novel problem in the realm of insurance mathematics. Existing literature concerning the market consistent valuation of insurance technical provisions includes [1,4,6,7,8,5], as-well as references therein. In particular, [4,6] follow the general idea of disentangling insurance cash flows into a hedgeable and a non-hedgeable part.…”

mentioning

confidence: 99%

Estimation of future discretionary benefits in traditional life insurance

Gach,

Hochgerner

2021

Preprint

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In the context of traditional life insurance, the future discretionary benefits (F DB), which are a central item for Solvency II reporting, are generally calculated by computationally expensive Monte Carlo algorithms. We derive analytic formulas for lower and upper bounds for the F DB. This yields an estimation interval for the F DB, and the average of lower and upper bound is a simple estimator. These formulae are designed for real world applications, and we compare the results to publicly available reporting data.

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“…In this case, some (generally imperfect) hedging of S by Y is possible and typically a two-step approach is followed (see Möhr, 2011 andAlbrecher et al, 2018). First, the insurer determines a hedging portfolio that is as close as possible to the liability S. To measure "closeness", the most popular objective function is the quadratic loss function, providing a trading strategy that minimises the L 2 -distance between the liability and the hedging portfolio (see Pelsser and Schweizer, 2016):…”

Section: Two-step Valuation With a Quadratic Loss Functionmentioning

confidence: 99%

Insurance valuation: A two-step generalised regression approach

Barigou¹,

Bignozzi²,

Tsanakas³

2020

Preprint

View full text Add to dashboard Cite

Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile.First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme.The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.

show abstract

Asset-liability management for long-term insurance business

Cited by 19 publications

References 37 publications

Insurance Valuation: A Two-Step Generalised Regression Approach

Insurance Valuation: A Two-Step Generalised Regression Approach

Estimation of future discretionary benefits in traditional life insurance

Insurance valuation: A two-step generalised regression approach

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