Related papers: Non-linear filtering and optimal investment under …
We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value…
In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the num\'eraire-based model and work with utility…
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by…
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution…
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization…
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial…
Stochastic volatility (SV) models mimic many of the stylized facts attributed to time series of asset returns, while maintaining conceptual simplicity. The commonly made assumption of conditionally normally distributed or…
We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local)…
In this paper, we investigate a portfolio selection problem with transaction costs under a two-factor stochastic volatility structure, where volatility follows a mean-reverting process with a stochastic mean-reversion level. The model…
We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…
We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual…
In this paper, we study the mean-variance portfolio selection problem under partial information with drift uncertainty. First we show that the market model is complete even in this case while the information is not complete and the drift is…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
Stochastic optimal control of dynamical systems is a crucial challenge in sequential decision-making. Recently, control-as-inference approaches have had considerable success, providing a viable risk-sensitive framework to address the…
Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
The econophysics approach to socio-economic systems is based on the assumption of their complexity. Such assumption inevitably lead to another assumption, namely that underlying interconnections within socio-economic systems, particularly…
In this paper, we study a non-linear filtering problem in the presence of signal model uncertainty. The model ambiguity is characterized by a class of probability measures from which the true one is taken. After interchanging the order of…
A nonlinear algebraic equation system of two variables is numerically solved, which is derived from a nonlinear algebraic equation system of four variables, that corresponds to a mathematical model related to investment under conditions of…
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the…