2014/03/17 by Kristina Rognlien Dahl, Salah-Eldin A. Mohammed, Dahl, Kristina R. +5
Economics, Econometrics and Finance · Physics and Astronomy · #34K50 #60H07 #60J75 #93E20 #93EXX #Advanced Thermodynamics and Statistical Mechanics #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1403.4034
openalex publication_date 2014/03/17 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
In this article we consider a stochastic optimal control problem where the\ndynamics of the state process, X(t), is a controlled stochastic differential\nequation with jumps, delay and \noisy memory. The term noisy memory is,\nto the best of our knowledge, new. By this we mean that the dynamics of X(t)\ndepend on \∫t-\δt X(s) dB(s) (where B(t) is a Brownian motion).\nHence, the dependence is noisy because of the Brownian motion, and it involves\nmemory due to the influence from the previous values of the state process.\n We derive necessary and sufficient maximum principles for this stochastic\ncontrol problem in two different ways, resulting in two sets of maximum\nprinciples. The first set of maximum principles is derived using Malliavin\ncalculus techniques, while the second set comes from reduction to a discrete\ndelay optimal control problem, and application of previously known results by\n Oksendal, Sulem and Zhang. The maximum principles also apply to the case\nwhere the controller only has partial information, in the sense that the\nadmissible controls are adapted to a sub-\σ-algebra of the natural\nfiltration.\n