aasmunhs

• Sande, Åsmund Hausken (2024). Ergodic Estimation and Model Assessment for Dynamic Exceedance Times. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2406.11347. Full text in Research Archive
• Sande, Åsmund Hausken & Wind, Johan Sokrates (2024). Minimal Convex Environmental Contours. SMAI Journal of Computational Mathematics (SMAI-JCM). 10, p. 55–83. doi: 10.5802/smai-jcm.106. Full text in Research Archive
• Banos, David Ruiz; Sande, Åsmund Hausken & Sgarra, Carlo (2023). Guaranteed Minimum Maturity Benefits in a Self-Exciting Stochastic Mortality Model: Pricing, Estimation and Calibration. North American Actuarial Journal (NAAJ). ISSN 1092-0277. 28(4), p. 744–771. doi: 10.1080/10920277.2023.2254836. Full text in Research Archive Show summary

  The guaranteed minimum maturity benefit (GMMB) is quite a popular feature embedded in several unit-linked policies offered by insurance companies. The value of this benefit depends on several processes assumed to describe both the mortality and the financial dynamics, typically represented by interest rates and by the fund associated to the unit-linked policy. A large literature is devoted to the valuation of GMMB for different mortality models, in particular when the mortality dynamics is described by affine models of diffusion type. In the present article we assume a self-exciting behavior for the mortality dynamics, described by a Hawkes-type process with exponential kernel. This allows us to keep both the Markov and affine features but introduces jumps with a stochastic intensity. These types of dynamics, exhibiting a jump clustering property, are quite convenient for describing mortality in some critical situations, like epidemics, where contagion phenomena make the probability of jump arrivals higher whenever a jump occurs. By assuming diffusion-type dynamics for both the fund and the interest rate and introducing all of the possible correlations among the diffusion processes necessary to obtain realistic dynamics, we take advantage of the affine features of the model proposed and compute in a semi-explicit form the value of a GMMB. Lastly, we calibrate our model and perform an empirical analysis to determine the effects of excess mortality on GMMB prices as well as a death benefit portfolio.

• Sande, Åsmund Hausken (2023). Convex environmental contours for non-stationary processes. Ocean Engineering. ISSN 0029-8018. 292. doi: 10.1016/j.oceaneng.2023.116615. Full text in Research Archive Show summary

  Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we consider convex contours based on the assumption of convex failure sets. We provide a rigorous foundation for the existence of such contours when the underlying environmental factors are modelled by a general, possibly non-stationary, process. This constitutes a generalisation of existing theory and is done to properly account for empirically observed increases in extreme sea-states. Two definitions are proposed, based respectively on averages or quantiles of exceedence times, along with minimal conditions on the environmental processes to guarantee existence. In order to illustrate these methods we give two examples, including an empirical study containing a method for constructing contours based on the presented theory.

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