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Partial Differential Equations

827 citations0/0 files storedEncyclopedia of Quantitative Finance

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Differential Equations and Boundary Problems

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Abstract This survey article outlines the various contexts where partial differential equations (PDEs) arise in finance. We discuss, in particular, option pricing, portfolio optimization, and calibration from the PDE viewpoint, and indicate further issues for PDE in finance.

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1973The Pricing of Options and Corporate Liabilities 1973Theory of Rational Option Pricing 1971Optimum consumption and portfolio rules in a continuous-time model 1979Martingales and arbitrage in multiperiod securities markets 1981Martingales and stochastic integrals in the theory of continuous trading 1997Backward Stochastic Differential Equations in Finance 1994Controlled markov processes and viscosity solutions

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