Obratne stohastične diferencialne enačbe : magistrsko delo

Leskovšek Kunc, Anja (author), Perman, Mihael (mentor)

Obratne stohastične diferencialne enačbe so poseben tip stohastičnih diferencialnih enačb, pri katerih imamo dano končno vrednost, ki se uporabljajo v finančnih modelih, ekonomskih problemih, stohastični kontroli, stohastičnih diferencialnih igrah itd. V tem delu si bomo pogledali, pod katerimi pogoji obstaja enolična rešitev za obratne stohastične diferencialne enačbe in nekaj primerov iz financ. Nato bomo definirali stohastično kontrolo ter dve glavni metodi, s katerima jo lahko rešujemo: dinamično programiranje ter Pontrjaginov stohastični princip maksimuma. Na koncu si bomo pogledali povezavo med obratnimi stohastičnimi diferencialnimi enačbami in stohastično kontrolo.

• Language: Slovenian
• Keywords: obratne stohastične diferencialne enačbe, stohastična kontrola, Hamiltonian sistema, dinamično programiranje, Pontrjaginov stohastični princip maksimuma.
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-135068
• UDC: 519.2
• COBISS.SI-ID: 98100483
• Publication date in RUL: 19.02.2022

LESKOVŠEK KUNC, Anja, 2022, Obratne stohastične diferencialne enačbe : magistrsko delo [online]. Master’s thesis. [Accessed 23 July 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=135068

Secondary language

• Language: English
• Title: Backward stochastic differential equations

Abstract

Backward stochastic differential equations are a special type of stochastic differential equations, in which the terminal value is already given, that are used in financial models, economic problems, stochastic control, stochastic differential games, etc. In this thesis we are going to look at the conditions under which there is a unique solution for the backward stochastic differential equations and some examples from finance. Then we will define stochastic control and two main methods with which we can solve it. These methods are dynamic programming and Pontryagin stochastic maximum principle. At the end, we will take a look at the connection between backward stochastic differential equations and stochastic control.

• Keywords: backward stochastic differential equations, stochastic control, the Hamiltonian of the system, dynamic programming, Pontryagin stochastic maximum principle.