In this paper, the optimal control of non-linear switching system is investigated without knowing dynamics. First, Hamilton-Jacobi-Bellman (HJB) equation derived with consideration hybrid action space. Then, a novel data-based Q-Iearning (HQL) algorithm proposed to find solution in an iterative manner. addition, theoretical analysis provided illustrate convergence and optimality algorithm. Fina...

An optimal control problem is considered for a stochastic differential equation with the cost functional determined by backward Volterra integral (BSVIE, short). This kind of can cover general discounting (including exponential and non-exponential) situations recursive feature. It known that such time-inconsistent in general. Therefore, instead finding global control, we look time-consistent lo...

We propose a method for calibrating a volatility surface that matches option prices using an entropy-inspired framework. Starting with a stochastic volatility model for asset prices, we cast the estimation problem as a variational one and we derive a Hamilton-Jacobi-Bellman (HJB) equation for the volatility surface. We study the asymptotics of the HJB equation assuming that the stochastic volat...

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic control problem to a complete observati...

Hysteresis in smart materials hinders their wider applicability in actuators. The low dimensional hysteresis models for these materials are hybrid systems with both controlled switching and autonomous switching. In particular, they belong to the class of Duhem hysteresis models and can be formulated as systems with both continuous and switching controls. In this paper, we study the control meth...

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

<p style='text-indent:20px;'>This paper studies the optimal portfolio selection for defined contribution (DC) pension fund with mispricing. We adopt general hyperbolic absolute risk averse (HARA) utility to describe performance of managers. The financial market comprises a risk-free asset, pair mispriced stocks, and index. Using dynamic programming approach, we construct Hamilton-Jacobi-B...

In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general insurance models to queueing theory. The main novel point of such a control problem is that by changing the jump size of the system, one essentially changes the...

In this paper, we investigate a fully nonlinear evolutionary Hamilton–Jacobi–Bellman (HJB) parabolic equation utilizing the monotone operator technique. We consider HJB arising from portfolio optimization selection, where goal is to maximize conditional expected value of terminal utility portfolio. The transformed into quasilinear using so-called Riccati transformation method. can be viewed as ...

This work aims to model the optimal control of dike heights. The control problem leads to so-called Hamilton-Jacobi-Bellman (HJB) variational inequalities, where the dike-increase and reinforcement times act as input quantities to the control problem. The HJB equations are solved numerically with an Essentially Non-Oscillatory (ENO) method. The ENO methodology is originally intended for hyperbo...