Related papers: Optimal execution with dynamic risk adjustment
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markov regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markov regime…
We build an optimal portfolio liquidation model for OTC markets, aiming at minimizing the trading costs via the choice of the liquidation time. We work in the Locally Linear Order Book framework of \cite{toth2011anomalous} to obtain the…
This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with…
In this work, we consider the optimal portfolio selection problem under hard constraints on trading volume amounts when the dynamics of the risky asset returns are governed by a discrete-time approximation of the Markov-modulated geometric…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the…
We analyze a continuous-time optimal trade execution problem in multiple assets where the price impact and the resilience can be matrix-valued stochastic processes that incorporate cross-impact effects. In addition, we allow for stochastic…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
When executing their orders, investors are proposed different strategies by brokers and investment banks. Most orders are executed using VWAP algorithms. Other basic execution strategies include POV (also called PVol) -- for percentage of…
We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
This paper considers an optimal control of a big financial company with debt liability under bankrupt probability constraints. The company, which faces constant liability payments and has choices to choose various production/business…
This paper presents several models addressing optimal portfolio choice, optimal portfolio liquidation, and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling…
Risk-bounded motion planning is an important yet difficult problem for safety-critical tasks. While existing mathematical programming methods offer theoretical guarantees in the context of constrained Markov decision processes, they either…
The optimization criterion for dividends from a risky business is most often formalized in terms of the expected present value of future dividends. That criterion disregards a potential, explicit demand for stability of dividends. In…
This paper is concerned with a kind of risk-sensitive optimal control problem for fully coupled forward-backward stochastic systems. The control variable enters the diffusion term of the state equation and the control domain is not…