相关论文: Theoretical and Numerical Analysis of an Optimal E…
Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild…
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…
In intertemporal settings, the multiattribute utility theory of Kihlstrom and Mirman suggests the application of a concave transform of the lifetime utility index. This construction, while allowing time and risk attitudes to be separated,…
We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with…
We investigate the large-time behavior of the value functions of the optimal control problems on the $n$-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of…
Optimal feedback controllers for nonlinear systems can be derived by solving the Hamilton-Jacobi-Bellman (HJB) equation. However, because the HJB is a nonlinear partial differential equation, numerical methods typically provide only…
Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods…
We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency 1/\Delta_n, with \Delta_n going to zero. The goal of this paper is to provide an estimator for the integral over [0,t] of a given function of the…
We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal…
In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market…
Optimal control problem is typically solved by first finding the value function through Hamilton-Jacobi equation (HJE) and then taking the minimizer of the Hamiltonian to obtain the control. In this work, instead of focusing on the value…
We consider the mean--variance portfolio optimization problem under the game theoretic framework and without risk-free assets. The problem is solved semi-explicitly by applying the extended Hamilton--Jacobi--Bellman equation. Although the…
The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potentially unmeasured confounding. In order to improve efficiency, multiple…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
We study an optimal investment and consumption problem over a finite-time horizon, in which an individual invests in a risk-free asset and a risky asset, and evaluate utility using a general utility function that exhibits loss aversion with…
We study the problem of estimating the value of a known smooth function $f$ at an unknown point $\boldsymbol{\mu} \in \mathbb{R}^n$, where each component $\mu_i$ can be sampled via a noisy oracle. Sampling more frequently components of…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
This paper studies the problem of optimally extracting nonrenewable natural resource in light of various financial and economic restrictions and constraints. Taking into account the fact that the market values of the main natural resources…
The modelling of financial markets presents a problem which is both theoretically challenging and practically important. The theoretical aspects concern the issue of market efficiency which may even have political implications…