Kamille Sofie Tågholt Gad

arXiv2020

Optimal variance stopping with linear diffusions

We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game theory by doing so. Our main result shows that an optimal solution can, in general case, be found among stopping times that are mixtures of two hitting times. This and other revealed phenomena together with suggested solution methods could be helpful when facing more complex non-linear optimal stopping problems. The results are illustrated by a few examples.

math.PR↗

arXiv2014

Reserve-Dependent Surrender

We study the modelling and valuation of surrender and other behavioural options in life insurance and pension. We place ourselves in between the two extremes of completely arbitrary intervention and optimal intervention by the policyholder. We present a method that is based on differential equations and that can be used to approximate contract values when policyholders exhibit optimal behaviour. This presentation includes a specification of sufficient conditions for both consistency of the model and convergence of the contract values. When not going to the limit in the approximation we obtain a technique for balancing off arbitrary and optimal behaviour in a simple, intuitive way. This leads to our suggestions for intervention models where one single parameter reflects the extent of rationality among policyholders. In a series of numerical examples we illustrate the impact of the rationality parameter on the contract values.

q-fin.MF↗