no code implementations • 13 Feb 2024 • Martin Herdegen, David Hobson, Alex S. L. Tse
The Merton investment-consumption problem is fundamental, both in the field of finance, and in stochastic control.
no code implementations • 13 Dec 2021 • Martin Herdegen, David Hobson, Joseph Jerome
Finally, we solve the optimal investment-consumption problem in a constant parameter financial market, where we optimise over the right-continuous attainable consumption streams that have a unique proper utility process associated to them.
no code implementations • 3 Nov 2021 • David Hobson, Gechun Liang, Edward Wang
This paper investigates the callable convertible bond problem in the presence of a liquidity constraint modelled by Poisson signals.
no code implementations • 14 Jul 2021 • David Hobson, Martin Herdegen, Joseph Jerome
The paper has three main goals: first, to provide a detailed introduction to infinite-horizon Epstein-Zin stochastic differential utility, including a discussion of which parameter combinations lead to a well-formulated problem; second, to prove existence and uniqueness of infinite horizon Epstein-Zin stochastic differential utility under a restriction on the parameters governing the agent's risk aversion and temporal variance aversion; and third, to provide a verification argument for the candidate optimal solution to the investment-consumption problem among all admissible consumption streams.
no code implementations • 9 Jun 2020 • Martin Herdegen, David Hobson, Joseph Jerome
In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black - Scholes - Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write down a candidate value function and to use a verification argument to prove that this is the solution to the problem.