Related papers: A Certainty Equivalent Merton Problem
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
This paper is devoted to solving a time-inconsistent risk-sensitive control problem with parameter $\e$ and its limit case ($\e\rightarrow0^+$) for countable-stated Markov decision processes (MDPs for short). Since the cost functional is…
The entropy regularization is inspired by information entropy from machine learning and the ideas of exploration and exploitation in reinforcement learning, which appears in the control problem to design an approximating algorithm for the…
We consider control of uncertain linear time-varying stochastic systems from the perspective of regret minimization. Specifically, we focus on the problem of designing a feedback controller that minimizes the loss relative to a clairvoyant…
In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the…
We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of…
Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…
We characterize optimal monetary policy when policy endogenously moves risk premia through redistribution across agents who differ in their willingness to bear risk. The analytical core is Marginal Risk Capacity, the covariance of monetary…
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and…
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
The Merton investment-consumption problem is fundamental, both in the field of finance, and in stochastic control. An important extension of the problem adds transaction costs, which is highly relevant from a financial perspective but also…
This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical…
The article's aim is to provide a solution to the equity premium puzzle with a derived model. The derived model which depends on Consumption Capital Asset Pricing Model gives a solution to the puzzle with the values of coefficient of…
We examine a multi-stage stochastic optimization problem characterized by stagewise-independent, decision-dependent noises with strict constraints. The problem assumes convexity in that, following a specific relaxation, it transforms into a…
We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the…