Polynomial diffusion models for life insurance liabilities

Biagini, Francesca; Zhang, Yinglin

doi:10.1016/j.insmatheco.2016.08.008

Cited by 21 publications

(26 citation statements)

References 39 publications

(78 reference statements)

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“…As already noticed in e.g. [3], [7] and [8], we recall that the three kinds of main products are special cases of payment streams by setting…”

Section: Robust Superhedging In the Reduced-form Frameworkmentioning

confidence: 99%

Reduced-form framework under model uncertainty

Biagini¹,

Zhang²

2019

Ann. Appl. Probab.

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In this paper we introduce a sublinear conditional expectation with respect to a family of possibly nondominated probability measures on a progressively enlarged filtration. In this way, we extend the classic reduced-form setting for credit and insurance markets to the case under model uncertainty, when we consider a family of priors possibly mutually singular to each other. Furthermore, we study the superhedging approach in continuous time for payment streams under model uncertainty, and establish several equivalent versions of dynamic robust superhedging duality. These results close the gap between robust framework for financial market, which is recently studied in an intensive way, and the one for credit and insurance markets, which is limited in the present literature only to some very specific cases.JEL Classification: C02, G10, G19

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“…As already noticed in e.g. [3], [7] and [8], we recall that the three kinds of main products are special cases of payment streams by setting…”

Section: Robust Superhedging In the Reduced-form Frameworkmentioning

confidence: 99%

Reduced-form framework under model uncertainty

Biagini¹,

Zhang²

2019

Ann. Appl. Probab.

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“…Investments in the longevity bonds also appear more irregular than the investment in asset S, due to the influence of the asset price's volatility on the strategies in (5.3). More details and further examples can be found in Biagini et al (2014).…”

Section: Annuity Contractmentioning

confidence: 99%

Risk‐minimization for Life Insurance Liabilities With Dependent Mortality Risk

Biagini

Botero

Schreiber

2015

Mathematical Finance

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In this paper, we study the pricing and hedging of typical life insurance liabilities for an insurance portfolio with dependent mortality risk by means of the well-known risk-minimization approach. As the insurance portfolio consists of individuals of different age cohorts in order to capture the cross-generational dependency structure of the portfolio, we introduce affine models for the mortality intensities based on Gaussian random fields that deliver analytically tractable results. We also provide specific examples consistent with historical mortality data and correlation structures. Main novelties of this work are the explicit computations of risk-minimizing strategies for life insurance liabilities written on an insurance portfolio composed of primary financial assets (a risky asset and a money market account) and a family of longevity bonds, and the simultaneous consideration of different age cohorts.

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“…Because of their inherent tractability, polynomial jump diffusions have played a prominent and growing role in a wide range of applications in finance. Examples include interest rates (Delbaen and Shirakawa 2002, Zhou 2003, Filipović et al 2017, stochastic volatility (Gourieroux andJasiak 2006, Ackerer et al 2018), exchange rates (Larsen and Sørensen 2007), life insurance liabilities (Biagini and Zhang 2016), variance swaps , credit risk (Ackerer and Filipović 2020a), dividend futures (Filipović and Willems 2019), commodities and electricity (Filipović et al 2018), stochastic portfolio theory (Cuchiero 2019), and economic equilibrium (Guasoni and Wong 2018). Properties of polynomial jump diffusions can also be brought to bear on computational and statistical methods, such as generalized method of moments and martingale estimating functions (Forman and Sørensen 2008), variance reduction (Cuchiero et al 2012), cubature , and quantization (Callegaro et al 2017).…”

Section: Introductionmentioning

confidence: 99%

Polynomial Jump-Diffusion Models

Filipović

Larsson

2020

Stochastic Systems

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We develop a comprehensive mathematical framework for polynomial jump diffusions in a semimartingale context, which nest affine jump diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and Lévy time change. We present a generic method for option pricing based on moment expansions. As an application, we introduce a large class of novel financial asset pricing models with excess log returns that are conditional Lévy based on polynomial jump diffusions. History: Former designation of this paper was SSy-2019-001.R1.

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Polynomial diffusion models for life insurance liabilities

Cited by 21 publications

References 39 publications

Reduced-form framework under model uncertainty

Reduced-form framework under model uncertainty

Risk‐minimization for Life Insurance Liabilities With Dependent Mortality Risk

Polynomial Jump-Diffusion Models

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