Risk-sensitive dynamic portfolio optimization with partial information on infinite time horizon.
type: Item
instance of: scholarly article
title: Risk-sensitive dynamic portfolio optimization with partial information on infinite time horizon.
zbMATH Open document ID: 1042.91048
author: Hideo Nagai
author: Shige Peng
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: The authors consider an optimal investment problem for a factor model as a risk-sensitive stochastic control problem, where the mean returns of individual securities are explicitly affected by economic factors defined as Gaussian processes. The market considered has \(m+1\geq 2\) securities and \(n\geq 1\) factors. It is assumed that the set of securities includes one bond whose price is defined by the ordinary differential equation \[ dS^0(t)=r(t)S^0(t) \,dt \] with a deterministic function \(r(t)\), and the other security prices and factors are assumed to satisfy stochastic differential equations \[ dS^i(t)=S^i(t) \left[(a+AX_t)^i dt + \sum_{k=1}^{n+m}\sigma_k^i dW_t^k\right], \] and \[ dX_t=(b+BX_t)dt+\Lambda dW_t. \] The investment strategies are supposed to be chosen without using information on factor processes, but by using only past information on security prices. The problem is formulated as a kind of stochastic control problem with partial information. The results concerning a finite-time horizon are summarized. Then the asymptotic behavior of the solution \(U(t,T)\) of the related inhomogeneous Riccati differential equation with the terminal condition is studied. Specific feature of asymptotics of the solution \(U(t,T)\) is stability as \(t\) and \(T-t\) tend to infinity, from which the asymptotic behavior of the value function and the optimal strategy of the problem on an infinite time horizon are obtained.
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 1906214
zbMATH Keywords: Ito calculus
zbMATH Keywords: partial differential equation
zbMATH Keywords: optimal investment problem
zbMATH Keywords: factor model
zbMATH Keywords: risk-sensitive stochastic control problem
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1015961160
OpenAlex ID: W1979086582
cites work: Q3997913
cites work: Optimal Control of Partially Observable Stochastic Systems with an Exponential-of-Integral Performance Index
cites work: Risk-sensitive dynamic asset management
cites work: Risk sensitive asset management with transaction costs
cites work: Q5562423
cites work: Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market
cites work: Q4868515
cites work: Q4086303
cites work: Optimal long term growth rate of expected utility of wealth
cites work: Risk-sensitive control and an optimal investment model.
cites work: A contribution to matrix quadratic equations
cites work: Risk-sensitive portfolio optimization on infinite time horizon
cites work: Q2707636
cites work: On a Matrix Riccati Equation of Stochastic Control
DOI: 10.1214/AOAP/1015961160
description: scientific article; zbMATH DE number 1906214