Some more concrete sources on Barrier option in the B&S setting and PDEs

• PDE methods for pricing barrier options (quite technical)
• Pricing Europ ean Barrier Options

More of a general remark to PDE approaches in finance

Ilya as far as I know the literature on that topic is quite limited. Solving a PDE means solving a PDE - it does not matter in which context. Most economists leave the solving of PDEs if they arise in a pricing context to pure mathematitians. This is why almost no finance book will teach you how to solve one explictly - this is either something you learn in pure math or physics or delgegate.

I think you are might be interested in "interfacing theorems" like Feynmen-Kac that establish the link between pricing and PDE.

Also to my knowledge there is no unifying PDE-based approach to pricing derivatives.

Still there are some books that have more extensive sections on PDE-theory e.g. PDE and Martingale Methods in Option Pricing You might also find the following report quite comprehensive. (The focus however is not on finding conrecte solution but rather on numerical schemes)

Some more concrete sources on Barrier option in the B&S setting and PDEs

• PDE methods for pricing barrier options (quite technical)
• Pricing Europ ean Barrier Options

More of a general remark to PDE approaches in finance

Ilya as far as I know the literature on that topic is quite limited. Solving a PDE means solving a PDE - it does not matter in which context. Most economists leave the solving of PDEs if they arise in a pricing context to pure mathematicians. This is why almost no finance book will teach you how to solve one explictly - this is either something you learn in pure math or physics or delgegate.

I think you are might be interested in "interfacing theorems" like Feynman-Kac that establish the link between pricing and PDE.

Also to my knowledge there is no unifying PDE-based approach to pricing derivatives.

Still there are some books that have more extensive sections on PDE-theory e.g. PDE and Martingale Methods in Option Pricing You might also find the following report quite comprehensive. (The focus however is not on finding closed-form solution but rather on numerical schemes)

More of a general remark to PDE approaches in finance

Ilya as far as I know the literature on that topic is quite limited. Solving a PDE means solving a PDE - it does not matter in which context. Most economists leave the solving of PDEs if they arise in a pricing context to pure mathematitians. This is why almost no finance book will teach you how to solve one explictly - this is either something you learn in pure math or physics or delgegate.

I think you are might be interested in "interfacing theorems" like Feynmen-Kac that establish the link between pricing and PDE.

Also to my knowledge there is no unifying PDE-based approach to pricing derivatives.

Still there are some books that have more extensive sections on PDE-theory e.g. PDE and Martingale Methods in Option Pricing You might also find the following report quite comprehensive. (The focus however is not on finding conrecte solution but rather on numerical schemes)

I will keep my eyes open and ask around - perhaps there is more.

Some more concrete sources on Barrier option in the B&S setting and PDEs

• PDE methods for pricing barrier options (quite technical)
• Pricing Europ ean Barrier Options

More of a general remark to PDE approaches in finance

Ilya as far as I know the literature on that topic is quite limited. Solving a PDE means solving a PDE - it does not matter in which context. Most economists leave the solving of PDEs if they arise in a pricing context to pure mathematitians. This is why almost no finance book will teach you how to solve one explictly - this is either something you learn in pure math or physics or delgegate.

I think you are might be interested in "interfacing theorems" like Feynmen-Kac that establish the link between pricing and PDE.

Also to my knowledge there is no unifying PDE-based approach to pricing derivatives.

Still there are some books that have more extensive sections on PDE-theory e.g. PDE and Martingale Methods in Option Pricing You might also find the following report quite comprehensive. (The focus however is not on finding conrecte solution but rather on numerical schemes)