Mean-variance optimal portfolios for Lévy processes and a singular stochastic control model for capacity expansion

In the first part of the thesis, the problem of determining the optimal capacity expansion strategy for a firm operating within a random economic environment is studied. The underlying market uncertainty is modelled by means of a general one-dimensional positive diffusion with possible absorption at...

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Main Author: Pasos, Jose E.
Published: London School of Economics and Political Science (University of London) 2018
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Online Access:https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.755854
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spelling ndltd-bl.uk-oai-ethos.bl.uk-7558542019-02-05T03:30:54ZMean-variance optimal portfolios for Lévy processes and a singular stochastic control model for capacity expansionPasos, Jose E.2018In the first part of the thesis, the problem of determining the optimal capacity expansion strategy for a firm operating within a random economic environment is studied. The underlying market uncertainty is modelled 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 twodimensional singular stochastic control problem that is explicitly solved. The general results are further illustrated in the special cases in which market uncertainty is modelled by a Brownian motion with drift, a geometric Brownian motion or a square-root mean-reverting process such as the one in the CIR model. The second part of the thesis presents a study of mean-variance portfolio selection for asset prices modelled by Lévy processes under conic constraints on trading strategies. In this context, the combination of the price processes’ jumps and the trading constraints gives rise to a new qualitative behaviour of the optimal strategies. The existence and the behaviour of the optimal strategies are related to different no-arbitrage conditions that can be directly expressed in terms of the Lévy triplet. This allows for a fairly complete characterisation of mean-variance optimal portfolios under conic constraints.QA MathematicsLondon School of Economics and Political Science (University of London)10.21953/lse.0ccqcg9tuwfehttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.755854http://etheses.lse.ac.uk/3771/Electronic Thesis or Dissertation
collection NDLTD
sources NDLTD
topic QA Mathematics
spellingShingle QA Mathematics
Pasos, Jose E.
Mean-variance optimal portfolios for Lévy processes and a singular stochastic control model for capacity expansion
description In the first part of the thesis, the problem of determining the optimal capacity expansion strategy for a firm operating within a random economic environment is studied. The underlying market uncertainty is modelled 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 twodimensional singular stochastic control problem that is explicitly solved. The general results are further illustrated in the special cases in which market uncertainty is modelled by a Brownian motion with drift, a geometric Brownian motion or a square-root mean-reverting process such as the one in the CIR model. The second part of the thesis presents a study of mean-variance portfolio selection for asset prices modelled by Lévy processes under conic constraints on trading strategies. In this context, the combination of the price processes’ jumps and the trading constraints gives rise to a new qualitative behaviour of the optimal strategies. The existence and the behaviour of the optimal strategies are related to different no-arbitrage conditions that can be directly expressed in terms of the Lévy triplet. This allows for a fairly complete characterisation of mean-variance optimal portfolios under conic constraints.
author Pasos, Jose E.
author_facet Pasos, Jose E.
author_sort Pasos, Jose E.
title Mean-variance optimal portfolios for Lévy processes and a singular stochastic control model for capacity expansion
title_short Mean-variance optimal portfolios for Lévy processes and a singular stochastic control model for capacity expansion
title_full Mean-variance optimal portfolios for Lévy processes and a singular stochastic control model for capacity expansion
title_fullStr Mean-variance optimal portfolios for Lévy processes and a singular stochastic control model for capacity expansion
title_full_unstemmed Mean-variance optimal portfolios for Lévy processes and a singular stochastic control model for capacity expansion
title_sort mean-variance optimal portfolios for lévy processes and a singular stochastic control model for capacity expansion
publisher London School of Economics and Political Science (University of London)
publishDate 2018
url https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.755854
work_keys_str_mv AT pasosjosee meanvarianceoptimalportfoliosforlevyprocessesandasingularstochasticcontrolmodelforcapacityexpansion
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