The Principle-Agent Conflict Problem in a Continuous-Time Delegated Asset Management Model

This paper considers the principle-agent conflict problem in a continuous-time delegated asset management model when the investor and the fund manager are all risk-averse with risk sensitivity coefficients γ f and γ m , respectively. Suppose that the investor entrusts his money to the fund manager. The return of the investment is determined by the manager’s effort level and incentive strategy, but the benefit belongs to the investor. In order to encourage the manager to work hard, the investor will determine the manager’s salary according to the terminal income. This is a stochastic differential game problem, and the distribution of income between the manager and the investor is a key point to be solved in the custody model. The uncertain form of the incentive strategy implies that the problem is different from the classical stochastic optimal control problem. In this paper, we first express the investor’s incentive strategy in term of two auxiliary processes and turn this problem into a classical one. Then, we employ the dynamic programming principle to solve the problem.

BSDEs with Logarithmic Growth Driven by Brownian Motion and Poisson Random Measure and Connection to Stochastic Control Problem

In this paper, we study one-dimensional backward stochastic differential equations under logarithmic growth in the 𝑧-variable ( | z | ⁢ | ln ⁡ | z | | ) (\lvert z\rvert\sqrt{\lvert\ln\lvert z\rvert\rvert}) . We show the existence and the uniqueness of the solution when the noise is driven by a Brownian motion and an independent Poisson random measure. In addition, we highlight the connection of such BSDEs with stochastic optimal control problem, where we show the existence of an optimal strategy for the control problem.

Optimal Position and Attitude Control of Quadcopter Using Stochastic Differential Dynamic Programming with Input Saturation Constraints

This paper considers the position and attitude control of a quadcopter in the presence of stochastic disturbances. Basic quadcopter dynamics is modeled as a nonlinear stochastic system described by a stochastic differential equation. Subsequently, the position and attitude control is formulated as a nonlinear stochastic optimal control problem with input saturation constraints. To solve this problem, a continuous-time stochastic differential dynamic programming (DDP) method with input saturation constraints is newly proposed. Finally, numerical simulations demonstrate the effectiveness of the proposed method by comparing it with the linear quadratic Gaussian and the deterministic DDP with input saturation constraints.

Optimal Control of the FitzHugh–Nagumo Stochastic Model with Nonlinear Diffusion

We consider the existence and first order conditions of optimality for a stochastic optimal control problem inspired by the celebrated FitzHugh–Nagumo model, with nonlinear diffusion term, perturbed by a linear multiplicative Brownian-type noise. The main novelty of the present paper relies on the application of the rescaling method which allows us to reduce the original problem to a random optimal one.

Stochastic maximum principle for systems driven by local martingales with spatial parameters

<p style='text-indent:20px;'>We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the stochastic maximum principle as the necessary condition for an optimal control, and we also prove its sufficiency under proper conditions. The stochastic linear quadratic problem in this setting is also discussed.</p>

Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems

The aim of this paper is to investigate a class of nonlinear stochastic reaction-diffusion systems involving fractional Laplacian in a bounded domain. First, the existence and uniqueness of weak solutions are proved by using Galërkin’s method. Second, the existence of optimal controls for the corresponding stochastic optimal control problem is obtained. Finally, several examples are provided to demonstrate the theoretical results.