Utility maximisation and utility indifference price for exponential semi-martingale models and HARA utilities
type: Item
instance of: scholarly article
title: Utility maximisation and utility indifference price for exponential semi-martingale models and HARA utilities
zbMATH Open document ID: 1403.91338
DOI: 10.1134/S0081543814080057
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2015-08-20T00:00:00Z
review text: The authors consider the utility maximisation problem for semi-martingale models and HARA (hyperbolic absolute risk aversion) utilities. The market is assumed to consist of one non-risky and two risky assets, possibly with jumps, represented as the stochastic exponents of two corresponding processes, \(X^{(1)}\) and \(X^{(2)}\). Process \(X^{(1)}\) us supposed to satisfy the Blumenthal--Getoor law at zero and possess predictable representation property. Corresponding market is supposed to be incomplete. The investor can trade the first asset until some maturity date and also has a European--type contingent claim for the second one, with the bigger maturity date. It may happen that the second asset can not be traded therefore the investor would like to evaluate the option for this asset. The price of the option in such a situation can be assessed by its indifferent price. So, it is possible to formulate the utility maximization problem in a natural setting. Using specific properties of HARA utilities, the authors reduce the initial maximization problem to the conditional one, which is solved by applying a dual approach. Then the solution of the conditional maximization problem is expressed via conditional information quantities related to HARA utilities, like the Kullback-Leibler information and Hellinger-type integrals. In turn, the information quantities are expressed in terms of information processes, which is helpful in indifference price calculus. Finally, equations for indifference prices are given. The results are applied to Black-Scholes models with correlated Brownian motions.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 6473880
zbMATH Keywords: utility maximisation problem
zbMATH Keywords: semi-martingale model
zbMATH Keywords: European--type contingent claim
zbMATH Keywords: incomplete market
zbMATH Keywords: indifferent price.
author: Anastasiya Ellanskaya
author: Lioudmila Vostrikova
MaRDI profile type: Publication
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full work available at URL: s0081543814080057
OpenAlex ID: W2170892542
description: scientific article; zbMATH DE number 6473880