A generic model for spouse's pensions with a view towards the calculation of liabilities

We introduce a generic model for spouse's pensions. The generic model allows for the modeling of various types of spouse's pensions with payments commencing at the death of the insured. We derive abstract formulas for cashflows and liabilities corresponding to common types of spouse's pensions. We show how the standard formulas from the Danish G82 concession can be obtained as a special case of our generic model. We also derive expressions for liabilities for spouse's pensions in models more advanced than found in the G82 concession. The generic nature of our model and results furthermore enable the calculation of cashflows and liabilities using simple estimates of marital behaviour among a population

Optimal Novikov-type criteria for local martingales with jumps

We consider local martingales $M$ with jumps larger than $a$ for some $a$ larger than or equal to -1, and prove Novikov-type criteria for the corresponding exponential local martingale to be a uniformly integrable martingale. We obtain criteria using both the quadratic variation and the predictable quadratic variation. We prove optimality of the coefficients in the criteria. As a corollary, we obtain a verbatim extension of the classical Novikov criterion for continuous local martingales to the case of local martingales with nonnegative jumps

Intervention in Ornstein-Uhlenbeck SDEs

We introduce a notion of intervention for stochastic differential equations and a corresponding causal interpretation. For the case of the Ornstein-Uhlenbeck SDE, we show that the SDE resulting from a simple type of intervention again is an Ornstein-Uhlenbeck SDE. We discuss criteria for the existence of a stationary distribution for the solution to the intervened SDE. We illustrate the effect of interventions by calculating the mean and variance in the stationary distribution of an intervened process in a particularly simple case.Comment: Extended version of article to be presented at the 18th EYS

Causal interpretation of stochastic differential equations

We give a causal interpretation of stochastic differential equations (SDEs) by defining the postintervention SDE resulting from an intervention in an SDE. We show that under Lipschitz conditions, the solution to the postintervention SDE is equal to a uniform limit in probability of postintervention structural equation models based on the Euler scheme of the original SDE, thus relating our definition to mainstream causal concepts. We prove that when the driving noise in the SDE is a L\'evy process, the postintervention distribution is identifiable from the generator of the SDE