Related papers: Implementing portfolio risk management and hedging…
Management of a portfolio that includes an illiquid asset is an important problem of modern mathematical finance. One of the ways to model illiquidity among others is to build an optimization problem and assume that one of the assets in a…
This work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately. A number of general classes of controller approximation error are analysed including…
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…
This paper examines a continuous time intertemporal consumption and portfolio choice problem with a stochastic differential utility preference of Epstein-Zin type for a robust investor, who worries about model misspecification and seeks…
This paper investigates a multidimensional non-homogeneous stochastic linear-quadratic optimal control problem featuring random coefficients and a terminal mean-field term in the cost functional, enabling its direct application to…
We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. This tutorial aims to introduce a number of different stochastic processes that can help in grasping the essential…
Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new…
In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature…
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR…
This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of…
We study the continuous time portfolio optimization model on the market where the mean returns of individual securities or asset categories are linearly dependent on underlying economic factors. We introduce the functional $Q_\gamma$…
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…
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…
This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…
This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable…
We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…