2 00 5 On some recent aspects of stochastic control and their applications ∗
نویسنده
چکیده
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman’s optimality principle and Pontryagin’s maximum principle, and their modern exposition with viscosity solutions and backward stochastic differential equations. Some original proofs are presented in a unifying context including degenerate singular control problems. We emphasize key results on characterization of optimal control for diffusion processes, with a view towards applications. Some examples in finance are detailed with their explicit solutions. We also discuss numerical issues and open questions.
منابع مشابه
Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications
In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...
متن کاملSe p 20 05 On some recent aspects of stochastic control theory and their applications ∗
This paper is a survey on some recent aspects and developments in stochastic control theory. We discuss the two main historical approaches, Bellman’s optimality principle and Pontryagin’s maximum principle, and their modern exposition with viscosity solutions and backward stochastic differential equations. Some original proofs are presented in a unifying context including degenerate singular co...
متن کاملMicroRNAs: Critical Regulators of mRNA Traffic and Translational Control with Promising Biotech and Therapeutic Applications
Context:MicroRNAs (miRNAs) are a class of short, endogenously-initiated, non-coding RNAs that post-transcriptionally control gene expression via translational repression or mRNA turnover. MiRNAs have attracted much attention in recent years as they play critical roles in gene expression and are promising tools with many biotech and therapeutic applications. The molecular mechanisms und...
متن کاملA Statistical Study of two Diffusion Processes on Torus and Their Applications
Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cann...
متن کاملApplications of TP2 Functions in Theory of Stochastic Orders: A Review of some Useful Results
In the literature on Statistical Reliability Theory and Stochastic Orders, several results based on theory of TP2/RR2 functions have been extensively used in establishing various properties. In this paper, we provide a review of some useful results in this direction and highlight connections between them.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008