On dynamic programming equations for utility indifference pricing under delta constraints
type: Item
instance of: scholarly article
title: On dynamic programming equations for utility indifference pricing under delta constraints
zbMATH Open document ID: 1214.91144
author: Takashi Adachi
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-05-10T00:00:00Z
review text: The author considers a financial market with a finite time horizon, driven by an ordinary stochastic differential equation. On this market, he studies a problem of utility indifference pricing for a small investor under portfolio constrains for a HARA utility function defined over the positive real line. The optimal investment problem is solved using an associated dynamic programming equation. The utility indifference price of a European contingent claim with a discounted payoff \(F\) is then shown to satisfy \(q(x,F) = x + v(F:u_0(x))\), where \(u_0(x)\) is the maximal expected utility for inital wealth \(x\) and \(-v(\cdot:y)\) is a convex risk measure. The author shows that \(v\) is the value of an associated stochastic game and characterizes it as a viscosity solution to an associated dynamic programming equation.
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 5886412
zbMATH Keywords: utility indifference price
zbMATH Keywords: portfolio constraint
zbMATH Keywords: HARA utility
zbMATH Keywords: dynamic programming equation
zbMATH Keywords: viscosity solution
reviewed by: G. M. Shevchenko
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.02.053
OpenAlex ID: W2023476536
cites work: Hedging costs for two large investors
cites work: Optimal consumption of the finite time horizon Ramsey problem
cites work: User’s guide to viscosity solutions of second order partial differential equations
cites work: Convex duality in constrained portfolio optimization
cites work: Utility maximization in incomplete markets with random endowment
cites work: Q4218383
cites work: Option valuation and hedging with basis risk
cites work: Exponential Hedging and Entropic Penalties
cites work: Q4032143
cites work: Introduction to a theory of value coherent with the no-arbitrage principle
cites work: Optional decompositions under constraints
cites work: Stochastic finance. An introduction in discrete time
cites work: Q3613975
cites work: Optimal investment with random endowments in incomplete markets.
cites work: ON UTILITY-BASED PRICING OF CONTINGENT CLAIMS IN INCOMPLETE MARKETS
cites work: On the pricing of contingent claims under constraints
cites work: Q4002114
cites work: The asymptotic elasticity of utility functions and optimal investment in incomplete markets
cites work: An example of indifference prices under exponential preferences
cites work: A valuation algorithm for indifference prices in incomplete markets
cites work: RISK INDIFFERENCE PRICING IN JUMP DIFFUSION MARKETS
cites work: OPTIMAL INVESTMENT WITH AN UNBOUNDED RANDOM ENDOWMENT AND UTILITY‐BASED PRICING
cites work: Pricing via utility maximization and entropy.
cites work: New proofs of a theorem of Komlós
cites work: On superhedging under delta constraints
cites work: Risk measure pricing and hedging in incomplete markets
DOI: 10.1016/J.JMAA.2011.02.053
Recommended article: Certainty equivalent and utility indifference pricing for incomplete preferences via convex vector optimization
Recommended article: Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market
Recommended article: Dynamic Programming Equations for Discounted Constrained Stochastic Control
Recommended article: Q4901054
Recommended article: A note on utility indifference pricing
Recommended article: On the Dynamic Programming Approach to Incentive Constraint Problems
Recommended article: DYNAMIC INDIFFERENCE VALUATION VIA CONVEX RISK MEASURES
Recommended article: Explicit Representations for Utility Indifference Prices
Recommended article: Dynamic convex duality in constrained utility maximization
description: scientific article; zbMATH DE number 5886412