Optimal contingent claims.
type: Item
instance of: scholarly article
title: Optimal contingent claims.
zbMATH Open document ID: 1040.91050
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: This is an elegant piece of mathematics applied to finance: a clear conceptualisation of a natural investment question. Suppose \(X\) is a certain underlying, i.e. a random variable. Financial markets value contingent claims on \(X\) by averaging and discounting with a certain probability \(P\). But ``you know'' that the ``right'' probability is different, namely, \(Q\). You want to invest a certain amount \(\alpha\), but you are willing to admit up to a certain risk level, \(\gamma\), and, of course, you would like to obtain out of this investment the maximum average return. Which derivative on \(X\) should you choose? In other terms you want to solve the following optimisation problem: -- Constraints: \(E_P(g(X))\leq \alpha\); \(V_Q(g(X))\leq \gamma^2\), -- Maximize \(E_Q(g(X))\) over ``all'' choices of \(g\). The answer is choose: \(g(x)= a+ b[{dQ\over dP}(x)]\) with appropriate choice of the constants \(a\) and \(b\). A number of quite interesting application follows.
reviewed by: J. L. Fernández
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 1906235
zbMATH Keywords: financial mathematic contingent claims
zbMATH Keywords: optimal investment
author: Andrius Jankunas
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1015345347
OpenAlex ID: W1993245151
cites work: Q4794153
cites work: Q5556832
cites work: Estimation of parameters of linear homogeneous stochastic differential equations
cites work: Estimation of parameters of linear stochastic difference equations.
cites work: Q4368791
cites work: Interest-rate option models: understanding, analysing and using models for exotic interest-rate options.
DOI: 10.1214/AOAP/1015345347
description: scientific article; zbMATH DE number 1906235