Last modified | |
Institution | University of Michigan |
Status | Postdoctoral Assistant Professor |
Contact | bernt@umich.edu |
Stochastics and its connections to Actuarial Science, Financial Mathematics and Statistics. Contributions made in the field of Filtering, Stochastic Differential Equations and Diffusions, Modelling, Measure Theory, and Optimal Control. Long-term goals include to develop new Stochastic tools beyond Itô Calculus.
Imagine a retiree who purchased an annuity and passes away instantly. In this case, the retiree surrendered their savings without any payoff from the annuity. Intuitively, the heirs of the retiree should receive the majority of the savings back (bequest). Only over time, while the retiree is subject to the annuity contract, the bequest should decrease. In particular, this study analyzes bequest in pooled annuity products not as balancing out two contradicting benefits but as insurance against an unexpected early death.
Tontines are well-understood under the assumption of constant market returns and a perfect pool. However the literature lacks in understanding the impact of fluctuating market returns and realized mortality rates. We analyze how many members a tontine need in order to deliver a stable income for life. We aim for practical answers that shall be used in the future for pension products.
Combining the best of drawdown and annuity, the investment returns and the longevity credits, tontines offer a great alternative to current pension products. Promoting tontines, we analyze the effect of a bequest motive on the decision to invest in a tontine. We formulate an investment problem where a pensioner chooses the percentage of wealth in the tontine, an investment strategy and their consumption rate. The investment problem is formulated such that the optimal strategy maximizes the utility of lifetime consumption and the left behind bequest. We show that, for a risk-averse investor, the percentage in the tontine is around 80% for a wide range of risk aversion and different bequest motives.
We solve a general optimal stopping problem involving generalized drift and show how the Principle of Smooth Fit is violated for specific choices of the problem data. We build on existing results from Lamberton and Zervos (2013). This is a technical analysis involving the concept of difference-of-two-convex-functions instead of twice-differentiable-functions.
The authors are part of the research project ”Minimising Longevity and Investment Risk while Optimizing Future Pension Plans”. This paper was written to familiarize the project team with the existing knowledge on decumulation strategies for pension funds. Here, highlighting important ideas and identifying promising areas for future research has been given most attention. On the other hand, topics related to implementation such as taxation or solvency or regulation has been given less attention.
In reality the flow of information arrives on a discrete time grid rather than it arrives in a continuous stream. Empirically there is no difference between models which have the same distribution at this grid. Therefore, we introduce a new class of continuous processes, the Itô semi-diffusions. These processes are modelled by a homogenous SDE between grid points, and have a prescribed distribution at grid points.
We consider the solvability of SDEs with homogeneous coefficients which are reflected in a càdlàg function. Our main idea is to use methods from Engelbert and Schmidt to show that under mild assumptions on drift and volatility the problem reduces to solve a Skorokhod-type problem. In particular, we can deal with non-Lipschitz coefficients.
We consider the problem to predict a stochastic intensity of a jump process given that we observe the occurrence of jumps in time. Under suitable integrability constraints, the literature provides already the means to deal with such problems in a general context. Our contribution is to point out that for a specific class of jump processes, the Cox-processes, these restrictions are not actually needed.
In this paper about market weights, the authors characterised polynomial jump-diffusions on the unit simplex. Here, they encountered possible measures on the complex plane with vanishing complex moments. In case of a probability measure, I suggested a proof excluding such possibilities. In the corresponding paper, see the proof of Theorem 4.3, Type 4, establishing 4.2 also in case of n=2.