Optimal investment under behavioural criteria in incomplete markets
Rodriguez Villarreal, José Gregorio
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In this thesis a mathematical description and analysis of the Cumulative Prospect Theory is presented. Conditions that ensure well-posedness of the problem are provided, as well as existence results concerning optimal policies for discrete-time incomplete market models and for a family of diffusion market models. A brief outline of how this work is organised follows. In Chapter 2 important results on weak convergence and discrete time finance models are described, these facts form the main background to introduce in Chapter 3 the problem of optimal investment under the CPT theorem in a discrete time setting. We describe our model, present some assumptions and main results are derived. The second part of this work comprises the description of the martingale problem formulation of diffusion processes in Chapter 4. A key result on the limits and topological properties of the set of laws of a class of Itô processes is described in Chapter 5. Finally, we introduce a factor model that includes a class of stochastic volatility models, possibly with path-depending coefficients. Under this model, the problem of optimal investment with a behavioural investor is analysed and our main results on well-posedness and existence of optimal strategies are described under the framework of weak solutions. Further research and challenges when applying the techniques developed in this work are described.