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We propose a continuous time model for financial markets with proportional transactions costs and a continuum of risky assets. This is motivated by bond markets in which the continuum of assets corresponds to the continuum of possible…
For time-inconsistent stochastic controls in discrete time and finite horizon, an open problem in Bj\"ork and Murgoci (Finance Stoch, 2014) is the existence of an equilibrium control. A nonrandomized Borel measurable Markov equilibrium…
We study a portfolio selection problem in a continuous-time It\^o-Markov additive market with prices of financial assets described by Markov additive processes which combine L\'evy processes and regime switching models. Thus the model takes…
Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted…
With the network methods and random matrix theory, we investigate the interaction structure of communities in financial markets. In particular, based on the random matrix decomposition, we clarify that the local interactions between the…
We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this…
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to…
According to recent findings [1,2], empirical covariance matrices deduced from financial return series contain such a high amount of noise that, apart from a few large eigenvalues and the corresponding eigenvectors, their structure can…
This tutorial describes recently developed general optimality conditions for Markov Decision Processes that have significant applications to inventory control. In particular, these conditions imply the validity of optimality equations and…
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is…
We consider "time-of-use" pricing as a technique for matching supply and demand of temporal resources with the goal of maximizing social welfare. Relevant examples include energy, computing resources on a cloud computing platform, and…
Default risk calculus plays a crucial role in portfolio optimization when the risky asset is under threat of bankruptcy. However, traditional stochastic control techniques are not applicable in this scenario, and additional assumptions are…
Since decades, the data science community tries to propose prediction models of financial time series. Yet, driven by the rapid development of information technology and machine intelligence, the velocity of today's information leads to…
In this paper we develop models of asset return mean and covariance that depend on some observable market conditions, and use these to construct a trading policy that depends on these conditions, and the current portfolio holdings. After…
This paper investigates the time-varying risk-premium relation of the Chinese stock markets within the framework of cross-sectional momentum and contrarian effects by adopting the Capital Asset Pricing Model and the French-Fama three factor…
We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger…
Monte Carlo algorithms simulate some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the…
We study the time dependence of maximal spanning trees and asset graphs based on correlation matrices of stock returns. In these networks the nodes represent companies and links are related to the correlation coefficients between them.…
This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…
In an incomplete semimartingale model of a financial market, we consider several risk-averse financial agents who negotiate the price of a bundle of contingent claims. Assuming that the agents' risk preferences are modelled by convex…