MDP algorithms for portfolio optimization problems in pure jump markets
type: Item
instance of: scholarly article
title: MDP algorithms for portfolio optimization problems in pure jump markets
zbMATH Open document ID: 1199.91169
author: Nicole Bäuerle
author: Ulrich Rieder
published in: Finance and Stochastics
publication date: 2010-04-22T00:00:00Z
full work available at URL: https://publikationen.bibliothek.kit.edu/1000032916
review text: The authors consider the classical problem of maximizing the expected utility of the terminal wealth of a portfolio in a financial market with general utility function. A continuous-time pure jump market is considered. It is assumed that jumps in the stock prices arrive in accordance with a Poisson process and that the relative jumps heights of the stocks are independent and identically distributed random vectors. The behavior of the stock prices between jumps is purely deterministic. Thus, the price processes fall in the class of piece-wise deterministic Markov processes. With the help of an embedding procedure, the optimal control problem is solved by looking at a discrete-time contracting Markov decision process. It is proved that the value function is the unique fixed point of a dynamic programming operator and that the value iteration as well as the policy iteration holds. The existence of an optimal stationary portfolio is established.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 5697477
zbMATH Keywords: portfolio optimization
zbMATH Keywords: piecewise deterministic Markov processes
zbMATH Keywords: Markov decision process
zbMATH Keywords: operator fixed points
zbMATH Keywords: approximation algorithms
MaRDI profile type: Publication
OpenAlex ID: W2024680294
cites work: A dynamic programming algorithm for the optimal control of piecewise deterministic Markov processes
cites work: Portfolio Optimization With Markov-Modulated Stock Prices and Interest Rates
cites work: PORTFOLIO OPTIMIZATION WITH JUMPS AND UNOBSERVABLE INTENSITY PROCESS
cites work: Stochastic optimal control. The discrete time case
cites work: Q3136505
cites work: Q4032143
cites work: Q3378427
cites work: Convergence of utility functions and convergence of optimal strategies
cites work: Efficient Hedging When Asset Prices Follow A Geometric Poisson Process With Unknown Intensities
cites work: Q2703816
cites work: The Markov Chain Market
cites work: Applied stochastic control of jump diffusions.
cites work: Portfolio optimization with unobservable Markov-modulated drift process
cites work: Control of ruin probabilities by discrete-time investments
DOI: 10.1007/S00780-009-0093-0
Recommended article: Continuous-time mean-variance portfolio optimization in a jump-diffusion market
Recommended article: PORTFOLIO OPTIMIZATION WITH JUMPS AND UNOBSERVABLE INTENSITY PROCESS
Recommended article: Constrained LQ problem with a random jump and application to portfolio selection
Recommended article: A martingale approach to optimal portfolios with jump-diffusions
Recommended article: Game-theoretic optimal portfolios for jump diffusions
Recommended article: Optimal portfolio execution with a Markov chain approximation approach
Recommended article: Martingale Approach to Optimal Portfolio-Consumption Problems in Markov-Modulated Pure-Jump Models
Recommended article: OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS
Recommended article: Portfolio optimization for jump-diffusion risky assets with regime switching: a time-consistent approach
description: scientific article; zbMATH DE number 5697477