Remarks on the nonlinear Black-Scholes equations with the effect of transaction costs

DOI10.1007/s10690-010-9115-3zbMath1195.91157OpenAlexW2104490398MaRDI QIDQ1959135

Naoyuki Ishimura

Publication date: 6 October 2010

Published in: Asia-Pacific Financial Markets (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10690-010-9115-3

zbMATH Keywords

solvabilitynonlinear partial differential equationstransaction costs

Mathematics Subject Classification ID

Financial applications of other theories (91G80) Derivative securities (option pricing, hedging, etc.) (91G20) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)

Related Items (9)

Analysis of the nonlinear option pricing model under variable transaction costs ⋮ Unnamed Item ⋮ A closed-form approximation for the fractional Black-Scholes model with transaction costs ⋮ Partial differential integral equation model for pricing American option under multi state regime switching with jumps ⋮ A Leland model for delta hedging in central risk books ⋮ Operator splitting kernel based numerical method for a generalized Leland's model ⋮ On the Hoggard-Whalley-Wilmott equation for the pricing of options with transaction costs ⋮ The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost ⋮ Fitted strong stability-preserving schemes for the Black-Scholes-Barenblatt equation

Cites Work

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• The Pricing of Options and Corporate Liabilities
• Well-posedness of one-phase Stefan problems for sublinear heat equations
• Elliptic partial differential equations of second order
• A Black--Scholes option pricing model with transaction costs
• On the Hoggard-Whalley-Wilmott equation for the pricing of options with transaction costs
• On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile
• Optimal hedging of options with small but arbitrary transaction cost structure
• European Option Pricing with Transaction Costs
• The Mathematics of Financial Derivatives
• Arbitrage Theory in Continuous Time

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