Recent zbMATH articles in MSC 93E20https://zbmath.org/atom/cc/93E202024-03-13T18:33:02.981707ZWerkzeugApproximate optimal control of fractional impulsive partial stochastic differential inclusions driven by Rosenblatt processhttps://zbmath.org/1528.490232024-03-13T18:33:02.981707Z"Yan, Zuomao"https://zbmath.org/authors/?q=ai:yan.zuomaoSummary: In this paper, we study the approximate optimal control problems for a class of fractional partial stochastic differential inclusions driven by Rosenblatt process and non-instantaneous impulses in a Hilbert space. Firstly, we prove an existence result of mild solutions for the control systems by using stochastic analysis, the fractional calculus, the measure of noncompactness, properties of sectorial operators and fixed point theorems. Secondly, we derive the existence conditions of approximate solutions to optimal control problems governed by fractional impulsive partial stochastic differential control systems with the help of minimizing sequence method. Finally, an example is given for the illustration of the obtained theoretical results.Malliavin calculus for Lévy processes with applications to financehttps://zbmath.org/1528.600012024-03-13T18:33:02.981707Z"Di Nunno, Giulia"https://zbmath.org/authors/?q=ai:di-nunno.giulia"Øksendal, Bernt"https://zbmath.org/authors/?q=ai:oksendal.bernt-karsten"Proske, Frank"https://zbmath.org/authors/?q=ai:proske.frank-norbertPublisher's description: While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated.
Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems.
To allow more flexibility in the treatment of the mathematical tools, the generalization of Malliavin calculus to the white noise framework is also discussed.
This book is a valuable resource for graduate students, lecturers in stochastic analysis and applied researchers.A two-stage variational inequality formulation for a game theory network model for hospitalization in critic scenarioshttps://zbmath.org/1528.910172024-03-13T18:33:02.981707Z"Daniele, Patrizia"https://zbmath.org/authors/?q=ai:daniele.patrizia"Sciacca, Daniele"https://zbmath.org/authors/?q=ai:sciacca.danieleSummary: In this paper, we introduce the theoretical structure of a stochastic generalized Nash equilibrium model describing the competition among hospitals with first aid departments for the hospitalization in a disaster scenario. Each hospital with a first aid department has to solve a two-stage stochastic optimization problem, one before the declaration of the disaster scenario and one after the disaster advent, to determine the equilibrium hospitalization flows to dispatch to the other hospitals with first aid and/or to hospitals without emergency rooms in the network. We define the generalized Nash equilibria of the model and, particularly, we consider the variational equilibria which is obtained as the solution to a variational inequality problem. Finally, we present a basic numerical example to validate the effectiveness of the model.
For the entire collection see [Zbl 1497.68012].Investment-consumption-insurance optimisation problem with multiple habit formation and non-exponential discountinghttps://zbmath.org/1528.910692024-03-13T18:33:02.981707Z"Wang, Yike"https://zbmath.org/authors/?q=ai:wang.yike"Liu, Jingzhen"https://zbmath.org/authors/?q=ai:liu.jingzhen"Siu, Tak Kuen"https://zbmath.org/authors/?q=ai:siu.tak-kuenSummary: This paper is devoted to an investment-consumption and life insurance problem with habit formation and non-exponential discounting. General utility functions are employed to evaluate non-habitual consumption and bequest. Distinct from \textit{J. Liu} et al. [Math. Control Relat. Fields 10, No. 4, 761--783 (2020; Zbl 1461.91279)] for consumption habit and feedback control, we assume that past consumption and bequest amounts have an interaction in formulating their endogenous reference levels, and we seek open-loop controls for both the pre-commitment solution and the time-consistent solution. Since the model coefficients are allowed to be random, we use the stochastic maximum principle to solve our problems. For both the pre-commitment and the time-consistent solution, an analytical expression is obtained via a system of forward-backward stochastic differential equations. Additionally, when the model coefficients are Markovian, we show that our problem for open-loop control can also be reduced to solving a Hamilton-Jacobi-Bellman equation, and then we introduce a transformation method for solving the equation. In particular, we provide a semi-analytical solution with numerical results based on simulations for the constant relative risk aversion (CRRA) utility with hyperbolic discounting.Optimal finite-dimensional controller of the stochastic differential object's state by its output. I: Incomplete precise measurementshttps://zbmath.org/1528.932402024-03-13T18:33:02.981707Z"Rudenko, E. A."https://zbmath.org/authors/?q=ai:rudenko.e-aSummary: The well-known problem of synthesizing the optimal on the average and on given time interval of the inertial control law for a continuous stochastic object if only a part of its state variables are accurately measured is considered. Due to the practical unrealizability of its classical infinite-dimensional Stratonovich-Mortensen solution, it is proposed to limit ourselves to optimizing the structure of a finite-dimensional dynamic controller, whose order is chosen by the user. This finiteness allows using a truncated version of the a posteriori probability density that satisfies a deterministic partial differential integrodifferential equation. Using the Krotov extension principle, sufficient optimality conditions for the structural functions of the controller and the Lagrange-Pontryagin equation for finding their extremals are obtained. It is shown that in particular cases of the absence of measurements, complete measurements and taking into account only the values of incomplete measurements, the proposed controller turns out to be static (inertialess), and the relations for its synthesis coincide with the known ones. For a dynamic controller, algorithms for finding each of its structural functions are given.