A recursive approach to mortality-linked derivative pricing

Shang, Zhaoning; Goovaerts, Marc; Dhaene, Jan

doi:10.1016/j.insmatheco.2011.03.003

Cited by 17 publications

(9 citation statements)

References 29 publications

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“…If the function f Tx (t) is a linear combination of some other probability density functions, i.e., if (1.6) Now, combinations of exponential distributions are (weakly) dense in the space of all probability distributions on the positive axis (Dufresne 2007a, b;Ko and Ng 2007); see also Section 3 in Shang et al (2011). Thus, if we can find a formula for the expectation E[e −δτ b(S(τ ))], (1.7)…”

Section: Introductionmentioning

confidence: 99%

Valuing equity-linked death benefits and other contingent options: A discounted density approach

Gerber

Shiu

Yang

2012

Insurance: Mathematics and Economics

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Section: Introductionmentioning

confidence: 99%

Valuing equity-linked death benefits and other contingent options: A discounted density approach

Gerber

Shiu

Yang

2012

Insurance: Mathematics and Economics

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“…• Design and pricing of longevity-linked derivatives (e.g. Shang et al, 2011;Lin et al, 2013;Wang & Yang, 2013;Chuang & Brockett, 2014) and specifically survivor/longevity swaps (e.g. Dowd et al, 2006;Wang et al, , 2015, survivor/longevity forwards and swaptions (e.g.…”

Section: • Landg Executed Buy-ins With the Pearson Pension Plan (£500m mentioning

confidence: 99%

Longevity risk and capital markets: the 2018–19 update

Blake

Cairns²

2020

Ann. actuar. sci.

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“…Its applications to financial mathematics can be noticed in Linetsky (1997Linetsky ( , 2004Linetsky ( , 2007 and the refereed papers therein. More recently, Goovaerts et al (2012) constructed a recursive scheme for the Laplace transform of the transition density function of a diffusion process using the Feynmann-Kac formula, also see Shang et al (2011).…”

Section: Proposition 32 We Have the Feynmann-kac Formulamentioning

confidence: 99%

Moments of renewal shot-noise processes and their applications

Jang

Dassios

Zhao

2018

Scandinavian Actuarial Journal

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In this paper, we study the family of renewal shot-noise processes. The Feynmann-Kac formula is obtained based on the piecewise deterministic Markov process theory and the martingale methodology. We then derive the Laplace transforms of the conditional moments and asymptotic moments of the processes. In general, by inverting the Laplace transforms, the asymptotic moments and the first conditional moments can be derived explicitly, however, other conditional moments may need to be estimated numerically. As an example, we develop a very efficient and general algorithm of Monte Carlo exact simulation for estimating the second conditional moments. The results can be then easily transformed to the counterparts of discounted aggregate claims for insurance applications, and we apply the first two conditional moments for the actuarial net premium calculation. Similarly, they can also be applied to credit risk and reliability modelling. Numerical examples with four distribution choices for interarrival times are provided to illustrate how the models can be implemented.

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A recursive approach to mortality-linked derivative pricing

Cited by 17 publications

References 29 publications

Valuing equity-linked death benefits and other contingent options: A discounted density approach

Valuing equity-linked death benefits and other contingent options: A discounted density approach

Longevity risk and capital markets: the 2018–19 update

Moments of renewal shot-noise processes and their applications

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