PhD opportunitiesFor details see the Research tab.
Huamao Wang (2008-2010): „Optimal Portfolio Choice under Partial Information and Transaction Costs” (joint with K.R. Schenk-Hoppé)
Huamao studied an extension of the Black-Scholes model of a financial market in which investors do not know the drift coefficient (growth rate) and are faced with proportional transaction costs when adjusting their portfolios. It is well-known that, on one hand, the drift plays a prime role in making financial decisions, but, on the other hand, it is extremely difficult to estimate. Incorporating the estimation error in portfolio optimisation (via stochastic filtering) allows to design an investment strategy which deals with this problem in an optimal way. In this PhD, Huamao looked at the performance of other commonly applied portfolio methods in relation to the optimal strategy. The highlights of this research are: (1) the construction of a numerical scheme capable of tackling this stochastic control problem, (2) the analysis of implications of transaction costs and uncertainly about the drift on the performance of various portfolio strategies.
Zhidi Du (2009-2014): „Option pricing and hedging under liquidity costs” (joint with K.R. Schenk-Hoppé)
Zhidi explored numerically utility-indifferent pricing of financial derivatives on the market with convex transaction costs which represent purchase/sale costs due to the depth of the order book (illiquidity). She shows that writing an option may be beneficial when transation costs are present resulting in a price which is lower than the replicating price on a frictionless market. Zhidi demonstrated that illiquidity causes volatility smile similar to the one observed on the market.
Tongya Wang (2010-2014): „Behavioural Biases and Evolutionary Dynamics in an Agent-Based Financial Market” (joint with K.R. Schenk-Hoppé)
Tongya studied financial market dynamics in a framework which combines agent-based modelling and concepts from behavioural finance. His PhD thesis explores, in an agent-based financial market model, the interlinkage between investor heterogeneity, bounded rationality, behavioural biases and the aggregate market dynamics. He shows that the interaction between passive and active learning is crucial to understanding the market selection of dominant strategy or the survival of different strategies. Investors’ bounded rationality and behavioural biases in active learning and financial forecasting play an important role in shaping the market dynamics. Tongya's findings point to the causes of the persistence of market inefficiencies and a variety of stylised facts of financial market.
James Fung (2010-2015): „Agent-based modelling of financial networks” (joint with K.R. Schenk-Hoppé)
James studied financial networks comprising financial institutions (banks) linked via the interbank LIBOR market. He wanted to understand the implication of the network topology and financial regulation on the stability and efficiency of the financial system.
Zeyu He (2013-) „Stochastic control with time-inconsistent criteria” (joint with G. Aivaliotis and A.Yu. Veretennikov)
Stochastic control with criteria that do not allow for the use of Bellman's principle.
Lloyd Davies (2013-) „The role of storage in the grid integration of electricity from low-carbon sources” (joint with P. Taylor and T. Cockerill)
Applied project within Integrated MSc and PhD studies in Low Carbon Technologies looking at potential for integrating storage into electricity grid using methods of stochastic control mixed with detailed deterministic short-term optimal scheduling of generation.
Alessandro Balata (2015-) „Regression Monte Carlo and its Applications in Energy Management” (joint with T. Cockerill, P. Taylor)
Alessandro is developing regression Monte Carlo methods for optimal control of Markov chains and inventory models. His research problems were originally motivated by management of electricity networks and micro-grids, see his talk on TEDx Leeds: Shaping a more Sustainable Future with Mathematics.
Nikita Merkulov (2017-) „Non-zero sum games of optimal stopping” (joint with T. De Angelis)
Game theory is a cornerstone of modelling and understanding behaviour of interacting individuals. It has not only attracted a lot of attention from social sciences but also proved a rich ground for development of mathematical theory. Nikita will study non-zero sum games of stopping arising when individuals have different probability measures, i.e., different perceptions of the world.
Cheng Cai (2017-) „Timing problems in optimal trading and hedging” (joint with T. De Angelis and G. Aivaliotis)
Hedging and optimal investment in presence of market frictions and institutional constraints leading to optimal stopping/impulse control problems and singular control problems.