357 research outputs found
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 with jumps larger than for some
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
- …