arXiv subjects

Sven Haadem

Publications and source records attributed to Sven Haadem.

4 recordsLinked to original sources

arXiv2021

Optimal stopping, randomized stopping and singular control with partial information flow

The purpose of this paper is two-fold: We extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a filtration with no a priori assumed relation to the filtration of the process. We call these problems optimal stopping and randomized stopping with general information. Following an idea of Krylov [K] we introduce a special singular stochastic control problem with general information and show that this is also equivalent to the partial information optimal stopping and randomized stopping problems. Then we show that the solution of this singular control problem can be expressed in terms of partial information variational inequalities.

math.OC↗

arXiv2013

On the Construction and Malliavin Differentiability of Levy Noise Driven SDEs with Singular Coefficients

In this paper we introduce a new technique to construct unique strong solutions of SDEs with singular coefficients driven by certain Levy processes. Our method which is based on Malliavin calculus does not rely on a pathwise uniqueness argument. Furthermore, the approach, which provides a direct construction principle, grants the additional insight that the obtained solutions are Malliavin differentiable.

math.PR↗

arXiv2012

A maximum principle for fractional diffusion processes with infinite horizon

We prove a maximum principle for the problem of optimal control for a fractional diffusion with infinite horizon. Further, we show existence of fractional backward stochastic differential equations on infinite horizon. We illustrate our findings with an example.

math.OC↗

arXiv2012

Maximum principles for jump diffusion processes with infinite horizon

We prove maximum principles for the problem of optimal control for a jump diffusion with infinite horizon and partial information. The results are applied to partial information optimal consumption and portfolio problems in infinite horizon.

math.OC↗