# Leo Gumpert: Optimal dividends in with-profit insurance using stochastic control

**Time: **
Wed 2023-02-08 10.15

**Location: **
Room Mittag-Leffler, Albano

**Respondent: **
Leo Gumpert

**Supervisor: **
Kristoffer Lindensjö

**Abstract:**

We study optimal dividend payments and investments of the surplus of with-profit life insurance policies using continuous-time stochastic control. Under some simplifying assumptions, the control problem studied can be treated as a generalisation of the investment-consumption problem first set up and studied by Merton. We use the dynamic programming method, by which the control problem boils down to solving a second order partial differential equation (PDE) called a Hamilton-Jacobi- Bellman equation. We consider cases where the policy holders display constant relative risk aversion, which implies first that the PDE has a semi-explicit solution and second that the optimal investment process is constant. The optimal dividend process is linear in the surplus. We illustrate the results with simulations for a simple life annuity, where the PDE has an explicit solution.