Working papers

Irreversible capacity expansion with possible default. Joint work with Mihalis Zervos and Hessah Al Motairi.

Abstract

We consider the problem of determining the optimal capacity expansion strategy that a firm operating within a random economic environment should adopt. We modelmarket uncertainty by means of a general one-dimensional positive diffusion with possible absorption at 0. The objective is to maximise a performance criterion that involves a general running payoff function and associates a cost with each capacity increase up to the first hitting time of 0, at which time the firm defaults. The resulting optimisation problem takes the form of a degenerate two-dimensional singular stochastic control problem that we explicitly solve. We further illustrate our general results in the special cases where market uncertainty is modelled by a Brownian motion with drift, a geometric Brownian motion or a square-root process such as the one in the CIR model.

The Markowitz Problem under Convex Cone Constraints in Lévy models. Joint work with Christoph Czichowsky.

Abstract
The Markovitz problem consists of finding a portfolio allocation with maximum wealth under the constraint of having its variance below a prespecified treshold. We study this problem in a continuous time market driven by a (exponential) multidimensional Lévy process and with conic constraints: trading strategies must take values in a closed convex cone. We provide a characterisation of the solvability of the Markovitz problem in terms of the arbitrage opportunitites that might be present in the market. When solutions exist, our technique allows to describe them in feedback form.

Presentations

Capacity Expansion with Possible Default. [poster]
"London-Paris Bachelier Workshop on Mathematical Finance 2015". London, UK. November 2015

A model for irreversible stochastic investment with possible default. [slides]

  • "LSE Statistics postgraduate seminar". London, UK. November 2015.
  • "Frontiers in stochastic models for finance". Padova, Italy. February 2016.
  • "At the frontiers of quantitative finance". Edinburgh, UK. June 2016.
  • "World congress of the Bachelier finance society". New York, USA. July 2016.